The paper pursues a premise semantics for counterfactuals. The way conflicts are resolved in a premise semantics depends on the way the premises are divided up and lumped together. Are there deep and non-trivial principles guiding this process that might be worth exploring? The article explores a positive answer to this question, which is then taken up in much more detail in my 'An investigation of the lumps of thought', in particular in the 2012 version. -/- The article (...) has been reprinted without substantial changes in my 2012 'Modals and Conditionals. New and Revised Perspectives.'. (shrink)

Kolodny and MacFarlane (“Ifs and oughts,” JPhil 107(3)) and MacFarlane (Assessment sensitivity, Chapter 11) describe the distinctive behavior of deontic modals in deliberation. They highlight two main features that any semantic theory should account for. First, deontic modals are informational in the sense that relativity to a body of information is an essential part of their interpretation. Second, modus ponens should be invalid, and it should fail when such modals are involved. And they argue for an account that posits information-neutral (...) semantic values. In this paper, I provide an account of deontic modals that does not involve any deviation from standard possible world semantic values, yet can capture their distinctive semantic behavior. The key element of the proposal is a partition-based semantics that treats available information as placing a constraint on interpretation. (shrink)

The advocate of modal logic or relevant logic has traditionally argued that her preferred system offers the best regimentation of the theory of entailment. Essential to the projects of modal and relevant logic is the importation of non-truth-functional expressive resources into the object language on which the logic is defined. The most elegant technique for giving the semantics of such languages is that of frame semantics, a variation on which features the device of partitioned frames that divide 'points (...) of evaluation' into two types: normal points and abnormal points. This essay attempts to provide satisfying philosophical interpretations of the partitioned frame semantics for some weak modal logics and relevant logics. According to the current best interpretation, partitioned frame semantics are a kind of possible worlds semantics that appeal to 'logically impossible worlds' where the laws of logic may fail to hold. This is undermined by the fact that all of the target logics fail to satisfy criteria of expressibility needed to support the thesis that laws of logic fail to hold at abnormal points. This suggests that we should not look for a monistic interpretive paradigm for partitioned frame semantics. (shrink)

An important part of the Unified Medical Language System (UMLS) is its Semantic Network, consisting of 134 Semantic Types connected to each other by edges formed by one or more of 54 distinct Relation Types. This Network is however for many purposes overcomplex, and various groups have thus made attempts at simplification. Here we take this work further by simplifying the relations which involve the three Semantic Types – Diagnostic Procedure, Laboratory Procedure and Therapeutic or Preventive Procedure. We define operators (...) which can be used to generate terms instantiating types from this selected set when applied to terms designating certain other Semantic Types, including almost all the terms specifying clinical tasks. Usage of such operators thus provides a useful and economical way of specifying clinical tasks. The operators allow us to define a mapping between those types within the UMLS which do not represent clinical tasks and those which do. This mapping then provides a basis for an ontology of clinical tasks that can be used in the formulation of computer-interpretable clinical guideline models. (shrink)

This article proposes a model for route description dialogues based on the integration of the theories about route directions with those related to specific spatial instructions. This proposal is based empirically on a corpus of spoken Italian. The analysis of the corpus has shown that the basic dialogue strategy proposed by previous researchers requires further integration and elaboration. Also the model of spatial language developed in cognitive linguistics applies to the description of the giver's instructions and directions, despite the fact (...) that the literature in the field often overlooks this approach. This way of accounting for route descriptions is suitable to explain the lexicalization of the conceptualization of the displacements the follower must accomplish. A model of dialogue partitions integrated with the cognitive modelling of spatial language is proposed and supported by examples from the linguistic data. (shrink)

In this paper I propose a partition semantics for sentences containing objective predicates that takes into account the phenomenon of occasion-sensitivity associated with so-called Travis cases. The key idea is that the set of worlds in which a sentence is true has a more complex structure as a result of different ways in which it is made true. Different ways may have different capacities to support the attainment of a contextually salient domain goal. I suggest that goal-conduciveness decides (...) whether some utterance of a sentence is accepted as true on a particular occasion at a given world. The utterance will not be accepted as true at a world which belongs to a truth-maker which is less conducive to a contextually salient goal than other truth-makers. Finally, the proposed occasion-sensitive semantics is applied to some cases of disagreement and cancellability. (shrink)

There are some who defend a view of vagueness according to which there are intrinsically vague objects or attributes in reality. Here, in contrast, we defend a view of vagueness as a semantic property of names and predicates. All entities are crisp, on this view, but there are, for each vague name, multiple portions of reality that are equally good candidates for being its referent, and, for each vague predicate, multiple classes of objects that are equally good candidates for being (...) its extension. We provide a new formulation of these ideas in terms of a theory of granular partitions. We show that this theory provides a general framework within which we can understand the relation between vague terms and concepts on the one hand and correlated portions of reality on the other. We also sketch how it might be possible to formulate within this framework a theory of vagueness which dispenses with the notion of truth-value gaps and other artifacts of more familiar approaches. (shrink)

The literature on conditionals is rife with alternate formulations of the abstract semantics of conditional logic. Each formulation has its own advantages in terms of applications and generalizations; nevertheless, they are for the most part equivalent, in the sense that they underwrite the same range of logical systems. The purpose of the present note is to bring under this umbrella the partition semantics introduced by Brian Skyrms in (Skyrms, 1984).

Current theories make a distinction between two types of case, STRUCTURAL case and INHERENT (or LEXICAL) case (Chomsky 1981), similar to the older distinction between GRAMMATICAL and SEMANTIC case (Kuryłowicz 1964).1 Structural case is assumed to be assigned at S-structure in a purely configurational way, whereas inherent case is assigned at D-structure in possible dependence on the governing predicates’s lexical properties. It is well known that not all cases fall cleanly into this typology. In particular, there is a class of (...) cases that pattern syntactically with the structural cases, but are semantically conditioned. These cases however depend on different semantic conditions than inherent cases do: instead of being sensitive to the thematic relation that the NP bears to the verbal predicate, they are sensitive to the NP’s definiteness, animacy, or quantificational properties, or to the aspectual character of the VP, or to some combination of these factors. The Finnish partitive is a particularly clear instance of this apparently hybrid category of semantically conditioned structural case. (shrink)

In many natural languages, there are clear syntactic and/or intonational differences between declarative sentences, which are primarily used to provide information, and interrogative sentences, which are primarily used to request information. Most logical frameworks restrict their attention to the former. Those that are concerned with both usually assume a logical language that makes a clear syntactic distinction between declaratives and interrogatives, and usually assign different types of semantic values to these two types of sentences. A different approach has been taken (...) in recent work on inquisitive semantics. This approach does not take the basic syntactic distinction between declaratives and interrogatives as its starting point, but rather a new notion of meaning that captures both informative and inquisitive content in an integrated way. The standard way to treat the logical connectives in this approach is to associate them with the basic algebraic operations on these new types of meanings. For instance, conjunction and disjunction are treated as meet and join operators, just as in classical logic. This gives rise to a hybrid system, where sentences can be both informative and inquisitive at the same time, and there is no clearcut division between declaratives and interrogatives. It may seem that these two general approaches in the existing literature are quite incompatible. The main aim of this paper is to show that this is not the case. We develop an inquisitive semantics for a logical language that has a clearcut division between declaratives and interrogatives. We show that this language coincides in expressive power with the hybrid language that is standardly assumed in inquisitive semantics, we establish a sound and complete axiomatization for the associated logic, and we consider a natural enrichment of the system with presuppositional interrogatives. (shrink)

The paper examines Schopenhauer’s complex diagrams from the Berlin Lectures of the 1820 s, which show certain partitions of classes. Drawing upon ideas and techniques from logical geometry, we show that Schopenhauer’s partition diagrams systematically give rise to a special type of Aristotelian diagrams, viz. (strong) α -structures.

In this paper I provide a decompositional analysis of three kinds of plural indefinites in two related languages, European Spanish and Brazilian Portuguese. The three indefinites studied are bare plurals, the unos (Spanish)/uns (Portuguese) type, and the algunos (Spanish)/alguns (Portuguese) type. The paper concentrates on four properties: semantic plurality, positive polarity, partitivity, and event distribution. The logic underlying the analysis is that of compositionality, applied at the subword level: as items become bigger in form (with the addition of morphemes), they (...) also acquire more semantic properties. The paper proposes the “indefinite hierarchy", which establishes a set of components for languages to build their indefinites with, in a particular order. (shrink)

This paper gives a uniform account of the meaning of generalizations with explicit exceptions that employ the prepositions “but”, “except”, and “except for”. Our theory is that exceptives depend on generalizations, which can but need not be universal, whose generality they limit, and some of whose exceptions they comment on. Every generalization intrinsically partitions its domain of applicability into regular cases, which are as it says to expect, and exceptions, which are not. A generalization’s exceptions are instances that falsify it (...) if sufficiently prevalent. These two facts underpin the meaning of exceptives as combining a _generality claim_ with an _exception claim_, giving correct truth conditions for the several ways the three exceptive prepositions are used, and significantly improving on existing semantic accounts in the literature. We support this by analyzing a wide range of examples. The analysis applies whether or not the phrase following the exceptive preposition is a DP, and whether or not the generalization is expressed with a quantifier. We further argue that these exceptive prepositions are synonymous, contrary to the widely held view that a difference in meaning explains their different syntactic distributions. (shrink)

A general mathematical framework, based on countable partitions of Natural Numbers [1], is presented, that allows to provide a Semantics to propositional languages. It has the particularity of allowing both the valuations and the interpretation Sets for the connectives to discriminate complexity of the formulas. This allows different adequacy criteria to be used to assess formulas associated with the same connective, but that differ in their complexity. The presented method can be adapted potentially infinite number of connectives and truth (...) values, therefore, it can be considered a general framework to provide semantics to several of the known logic systems (eg, LC, L3 LP, FDE). The presented semantics allow to converge to different standard semantics if the separation complexity procedure is annulled. Therefore, it can be understood as a framework that allows greater precision (in complexity terms) with respect to formula satisfaction. Naturally, because of how it is built, it can be incorporated into non-deterministic semantics. The presented procedure also allows generating valuations that grant a different truth value to each formula of propositional language. As a positive side effect, our method allows a constructive proof of the equipotence between N and N^n for all Natural n. (shrink)

In this paper we examine partitioned interpretations of sentences with reciprocal expressions. We study the availability of partitioned readings with definite subjects and proper name conjunctions, and show new evidence that partitioned interpretations of simple reciprocal sentences are independent of the semantics of the reciprocal expression, and are exclusively determined by the interpretation of the subject.

The main aim of the thesis is to give a semantic account of implicit content – the kind of content that plays a crucial role in implicit communication. Implicit communication is a species of communication in which a speaker communicates certain contents that go over and above the contents retrievable from the linguistic meaning of the words used. The focus of the thesis is a certain kind of implicit communication involving locations (when sentences such as “It is raining” are used (...) to communicate that it is raining at a certain location) and judges (when sentences such as “Avocado is tasty” are used to communicate that avocado is tasty for a certain person, called “the judge”). The way the topic of implicit content is approached is via the notion, widespread in contemporary philosophy of language, of “unarticulated constituents”. The thesis contains an investigation of this notion, with the specific aim of disentangling the many senses it has been used and of providing a general definition of the notion. A direct product of this investigation is a partitioning of the logical space; three positions are then selected, which correspond to the main contenders in the current debate involving unarticulated constituents: truth-conditional semantics, truth-conditional pragmatics and relativism. The biggest part of the thesis is dedicated to investigating certain arguments that have surfaced in the debate between these positions, with the ultimate goal of proposing a relativist account of implicit content. The particular version of relativism offered consists in the combination of the claim that locations and judges are part of the circumstances of evaluation, rather than the content of utterances, with “the variadic functions approach” to certain natural language expressions. Also, several arguments against a truth-conditional semantic approach to predicates of personal taste are provided. (shrink)

Ontologies are the prime way of organizing data in the Semantic Web. Often, it is necessary to combine several, independently developed ontologies to obtain a complete representation of a domain of interest. The complementarity of existing ontologies can be leveraged by merging them. Existing approaches for ontology merging mostly implement a binary merge. However, with the growing number and size of relevant ontologies across domains, scalability becomes a central challenge. A multi-ontology merging technique offers a potential solution to this problem. (...) We present Co Merger, a scalable multiple ontologies merging method. It takes as input a set of source ontologies and existing mappings across them and generates a merged ontology. For efficient processing, rather than successively merging complete ontologies pairwise, we group related concepts across ontologies into partitions and merge first within and then across those partitions. In both steps, user-specified subsets of generic merge requirements (GMRs) are taken into account and used to optimize outputs. The experimental results on well-known datasets confirm the feasibility of our approach and demonstrate its superiority over binary strategies. A prototypical implementation is freely accessible through a live web portal. (shrink)

We present a cross-linguistically robust pattern of polyfunctionality between indefinite, partitive, and disanaphoric (‘another’) use of a single lexical item. In examining the connection between these different uses, we argue that a uniform semantics underlies all of them. We employ the salience theory of definiteness, with the specific implementation in a dynamic semantics with choice functions, to model the full spectrum of the attested uses without invoking implicit variables. The core meaning is the partitive implication, whereas the indefinite (...) and the discourse-familiar disanaphoric readings are underspecified in the semantics and are argued to be additional construals conditioned by discourse factors. The partitive meaning, however, is shown itself to be subject to variable pragmatic packaging across languages, from being a part of the truth conditions to a postsupposition. (shrink)

Logical geometry systematically studies Aristotelian diagrams, such as the classical square of oppositions and its extensions. These investigations rely heavily on the use of bitstrings, which are compact combinatorial representations of formulas that allow us to quickly determine their Aristotelian relations. However, because of their general nature, bitstrings can be applied to a wide variety of topics in philosophical logic beyond those of logical geometry. Hence, the main aim of this paper is to present a systematic technique for assigning bitstrings (...) to arbitrary finite fragments of formulas in arbitrary logical systems, and to study the logical and combinatorial properties of this technique. It is based on the partition of logical space that is induced by a given fragment, and sheds new light on a number of interesting issues, such as the logic-dependence of the Aristotelian relations and the subtle interplay between the Aristotelian and Boolean structure of logical fragments. Finally, the bitstring technique also allows us to systematically analyze fragments from contemporary logical systems, such as public announcement logic, which could not be done before. (shrink)

n the philosophy of language, there are many ongoing controversies that stem from relying too heavily on an utterance-based framework. The traditional approach of rigidly partitioning the utterance’s meaning into what is grammatically determined from what is not may not fully capture the complexity of human language in real-world communicative contexts. To address this issue, we suggest shifting focus toward a broader analysis level encompassing conversations and discourses. From this broader perspective, it is possible to obtain a more integrated view (...) of how linguistic and extra-linguistic aspects dynamically interact and thus reconsider semantics/pragmatics dichotomy as complementary dimensions. Meaning is not confined to linguistic structures alone but emerges from the dynamic interplay of words, sociocultural knowledge, discursive situations, and psychological dispositions of speakers. Substantiating this perspective calls for embracing an interdisciplinary approach that synthesizes research from various domains, including linguistics, cognitive psychology, and philosophy of language. This paper focuses on a particularly compelling case study: aphasia. Speeches produced by individuals with aphasia represent complex scenarios where the balance between linguistic and extra-linguistic aspects is notably compromised, often to the former’s detriment. Aphasics’ productions represent a vivid example of how the interpretation of speeches can be far from involving fixed and static operations. Instead, it entails continuously reallocating cognitive resources toward the most readily available and accessible sources for the speakers. This case study ultimately demonstrates that the influence of semantic and pragmatic processes in shaping and conveying meanings displays remarkable adaptability, continuously adjusting to the ever changing demands placed upon speakers. -/- . (shrink)

Presents a concise introduction to the partition analysis of questions and outlines a theory of answerhood based on that.

This paper investigates lexical mass-to-count and count-to-mass operators in Slavic languages, primarily Russian and Ukrainian, by exploring the distribution and semantic contribution of the suffix -_in_/-_yn_. The focus is on two uses of the suffix: the singulative turns mass nouns like _gorox_ ‘pea’ into count, denoting sets of natural units (e.g., _gorošina_ ‘a pea’), and the massifier applies to count nouns, such as _kon’_ ‘horse’, and turns them into mass (e.g., _konina_ ‘horsemeat’). It is proposed that each use of -_in_/-_yn_ (...) contributes a partition operator which triggers a new division into units of the original material part. It is further argued that the singulative and the massifier should be unified, given their (i) phonological identity, (ii) shared grammatical properties, and (iii) common semantic core. Under the proposed analysis, there is a single suffix that functions as an underspecified lexical partition shifter. (shrink)

In this paper I argue against a sharp separation of semantics from pragmatics. While it may be useful to consider semantics independently of pragmatics, in some cases this strategy may lead us astray. First, I make a methodological point. Competing semantic analyses are often presented as supported by competing semantic intuitions of native speakers. Functional considerations are pragmatic considerations which should affect our choice of semantics. These are inferences from the linguistic goals the speakers actually achieve to (...) the meanings their expressions must therefore have. Second, there are linguistic expressions whose semantic meaning is a function of their pragmatic uses. I consider two examples. First, the logicians' debate over the universal analysis of conditionals in natural language. The participants in the debate all ignore conditional forms other than the assertoric and subjunctive. In particular they ignore the conditional speech-act reading. The meaning of the conditional is related to its function: to restrict the commitment of a given speech-act to special conditions. A functional proof of the existence of such conditionals is given, thus showing that the different semantics account only for part of the relevant facts. The second example concerns vague terms. I claim that one of their main uses is to help us identify objects by reference not to their absolute properties but relative to their background. This function cannot be performed by the use of non-vague terms. Vague terms are context dependent and may in some contexts be used non-vaguely and refer to distinct objects in the discourse domain. In a way, what these terms end up denoting is a function of the use of predicates to partition a given domain. (shrink)

This paper offers a new unified theory about the meaning of the imperfective and progressive aspects that builds on earlier of analyses in the literature that treat the imperfective as denoting a universal quantifier (e.g. Bonomi, Linguist Philos, 20(5):469–514, 1997; Cipria and Roberts, Nat Lang Semant 8(4):297–347, 2000). It is shown that the problems associated with such an analysis can be overcome if the domain of the universal quantifier is taken to be a partition of a future extending interval (...) into equimeasured cells. Treating the partition-measure (the length of each partition-cell) as a contextually dependent variable allows for a unified treatment of the habitual and event-in-progress readings of the imperfective. It is argued that the contrast between the imperfective and the progressive has to do with whether the quantifier domain is a regular partition of the reference interval or a superinterval of the reference interval. (shrink)

Causal theories of content, a popular family of approaches to defining the content of mental states, commonly run afoul of two related and serious problems that prevent them from providing an adequate theory of mental content—the misrepresentation problem and the disjunction problem. In this paper, I present a causal theory of content, built on information theoretic tools, that solves these problems and provides a viable model of mental content. This is the greatest surprise reduction theory of content, which identifies the (...) content of a signal as the event the surprisal of which is most reduced by that signal. Conceptually, this amounts to the claim that the content of a signal is the event the probability of which has increased by the largest proportion, or the event that the signal makes the most less surprising to us. I develop the greatest surprise reduction theory of content in four stages. First, I introduce the general project of causal theories of content, and the challenges presented to this project by the misrepresentation and disjunction problems. Next, I review two recent and prominent causal theories of content and demonstrate the serious challenges faced by these approaches, both clarifying the need for a solution to the misrepresentation and disjunction problems and providing a conceptual background for the greatest surprise reduction theory. Then, I develop the greatest surprise reduction theory of content, demonstrate its ability to resolve the misrepresentation and disjunction problems, and explore some additional applications it may have. Finally, I conclude with a discussion of a particularly difficult challenge that remains to be addressed—the partition problem—and sketch a path to a potential solution. (shrink)

ABSTRACT We show that some PRO-sentences (sentences containing an unpronounced subject in an infinitive clause) appear to receive de re interpretations when they occur in suitable discourse contexts or linguistic environments. This finding is surprising given the received view that such sentences are unambiguously de se [Morgan. 1970. “On the Criterion of Identity for Noun Phrase Deletion.” Papers from the Sixth Regional Meeting of the Chicago Linguistics Society, Chicago, IL, 380–389; Chierchia. 1990. “Anaphora and Attitudes de se.” In Semantics (...) and Contextual Expression, edited by R. Bartsch, J. van Benthem, and P. van Emde Boas, 1–32. Dordrecht: Foris]. We argue that these apparent de re readings are not genuine readings assigned by the grammar, but rather arise via a pragmatic process that results in what we call ‘excluded entailments’. The interpretation of PRO-sentences thus shows a certain amount of pragmatic latitude that is reminiscent of other cases of non-literal language, such as examples of ‘pragmatic slack’ first discussed in Lasersohn [1999. “Pragmatic Halos.” Language 75: 522–551]. However, we show that there are crucial differences between the puzzling data at hand and more familiar cases of pragmatic slack, and argue that they constitute a different class of non-literal meaning that has received less attention in the literature. This class of meanings is akin to that introduced by the modifier ‘in effect’. Our view has consequences for semantic methodology, understanding the limits of non-literal language use and interpretation, and the division of labour between semantics and pragmatics in the analysis of attitude reports. (shrink)

The Knowability Paradox is a logical argument that, starting from the plainly innocent assumption that every true proposition is knowable, reaches the strong conclusion that every true proposition is known; i.e. if there are unknown truths, there are unknowable truths. The paradox has been considered a problem for every theory assuming the Knowability Principle, according to which all truths are knowable and, in particular, for semantic anti-realist theories. A well known criticism to the Knowability Paradox is the so called restriction (...) strategy. It bounds the scope of the universal quantification in (KP) to a set of formulas whose logical form avoids the paradoxical conclusion. Specifically, Tennant suggests to restrict the quantifier in (KP) to propositions whose knowledge is provably inconsistent. He calls them Anti-Cartesian propositions and distinguished them in three kinds. In this paper we will not be concerned with the soundness of the restriction proposal and the criticisms it has received. Rather, we are interested in analyzing the proposed distinction. We argue that Tennant’s distinction is problematic because it is not completely clear, it is not grounded on an adequate logical analysis, and it is incomplete. We suggest an alternative distinction, and we give some reasons for accepting it: it results logically grounded and more complete than Tennant’s one, inclusive of it and independent from non-epistemic notions. (shrink)

Traditional approaches to the semantics of questions analyze questions indirectly, via the notion of an answer. In recent work on inquisitive semantics, a different perspective is taken: the meaning of a question is equated with its resolution conditions, just like the meaning of a statement is traditionally equated with its truth-conditions. In this paper I argue that this proposal improves on previous approaches, combining the formal elegance and explanatory power of Groenendijk and Stokhof’s partition theory with the (...) greater generality afforded by answer-set theories. (shrink)

This paper investigates the prospects for a semantic theory that treats disjunction as a modal operator. Potential motivation for such a theory comes from the way in which modals embed within disjunctions. After reviewing some of the relevant data, I go on to distinguish a variety of modal theories of disjunction. I analyze these theories by considering pairs of conflicting desiderata, highlighting some of the tradeoffs they must face.

Wittgenstein took the _Tractatus Logico-Philosophicus_ to be eventually invalidated by logical atomism. Our main thesis is that it can be revalidated, provided that we subtract the thesis 2.02 (“The object is simple.”) from it: atoms are not simple objects but, rather, bits of information the objects are made of. Starting from an introductory discussion about what is meant by a ‘logic of colors’, an explanatory framework is then proposed in the form of a partition semantics. The philosophical problem (...) of Wittgenstein’s color-statements is reformulated accordingly, thus overcoming the trouble with logical atomism. A Boolean treatment is advanced to solve the initial difficulty and leads to two final results: Wittgenstein’s logic of colors requires a mereological understanding of the relations between colors in order to make sense; the analysis of psychophysical concepts like colors casts some additional doubt about the analytic–synthetic distinction, to the point of treating relations between colors as analytic a posteriori judgments. (shrink)

Semantics for logics with Topic Sensitive Intentional Modal operators require a structure, often a mereology, of topics. These structures have varied from mere semi-lattices and sets of partitions of possible worlds to collections of subalgebras. We will argue that a natural representation of topic is as vectors in a vector space. This idea is motivated by the use of vector space models in large language models. There, the relation between vectors corresponds to the semantic relation between the topics of (...) the words being modeled by the vectors. As such, we reconstruct a logic of conditional hyperintensional belief given in Özgün and Berto ( 2021 ), replacing their semi-lattice of topics with a vector space of topics. In these vector-based models, the containment relation of topics is given an intuitive reading that (unlike the semi-lattice reading) is straightforwardly compatible with a selection of modifications and extensions that we will discuss. We are offering a new semantics for a logic: the main upshots are a formal framework for topical vector spaces, and that the introduced semantics is philosophically satisfying. (shrink)

Taking the lead from orthodox quantum theory, I will introduce a handy generalization of the Boolean approach to propositions and questions: the orthoalgebraic framework. I will demonstrate that this formalism relates to a formal theory of questions (or ‘observables’ in the physicist’s jargon). This theory allows formulating attitude questions, which normally are non-commuting, i.e., the ordering of the questions affects the answer behavior of attitude questions. Further, it allows the expression of conditional questions such as “If Mary reads the book, (...) will she recommend it to Peter?”, and thus gives the framework the semantic power of raising issues and being informative at the same time. In the case of commuting observables, there are close similarities between the orthoalgebraic approach to questions and the Jäger/Hulstijn approach to question semantics. However, there are also differences between the two approaches even in case of commuting observables. The main difference is that the Jäger/Hulstijn approach relates to a partition theory of questions whereas the orthoalgebraic approach relates to a ‘decorated’ partition theory (i.e. the elements of the partition are decorated by certain semantic values). Surprisingly, the orthoalgebraic approach is able to overcome most of the difficulties of the Jäger/Hulstijn approach. Furthermore, the general approach is suitable to describe the different types of (non-commutative) attitude questions as investigated in modern survey research. Concluding, I will suggest that an active dialogue between the traditional model-theoretic approaches to semantics and the orthoalgebraic paradigm is mandatory. (shrink)

'Post this letter!' does not entail 'Post this letter or drink up my wine!' (the Ross Paradox) because one can be in a state with the content of the former without being in a state with the content of the latter; in turn, because the latter can rationalize drinking up my wine but the former cannot; in turn, because practical rationalization flows toward one's present situation, in contrast with the flow of theoretical rationalization from one's present situation. Formally, this is (...) implemented with a semantics for imperatives involving a partition to set up an issue of significance and a proposition to establish how to settle it. I characterize a series of languages and language-games to implement all this, and appeal to an 'endorsement-theoretic' conception of modals as quantifiers over mental states to explain why 'You must post this letter' does not entail 'You must either post this letter or drink up my wine'. (shrink)

This dissertation investigates the ways in which natural language restricts the domains of quantifiers. Adverbs of quantification are analyzed as quantifying over situations. The domain of quantifiers is pragmatically constrained: apparent processes of "semantic partition" are treated as pragmatic epiphenomena. The introductory Chapter 1 sketches some of the background of work on natural language quantification and begins the analysis of adverbial quantification over situations. Chapter 2 develops the central picture of "semantic partition" as a side-effect of pragmatic processes (...) of anaphora resolution. I argue that the apparent effects of topic/focus articulation and presuppositional information on the interpretation of quantifiers are not the result of a direct and local mechanism of sentence grammar. Instead, I develop an analysis where the link is established via the anaphoric dependence of quantifier domains on the discourse context. Chapter 3 discusses the analysis of conditional clauses as quantifier restrictors, concentrating on the question whether conditional clauses restrict quantifiers directly or indirectly. A treatment is explored which has if-clauses constrain the value of the hidden domain variable of the restricted quantifier. Chapter 4, on unless-clauses, and Chapter 5, on only if- and even if-clauses, present some issues in the compositional analysis of complex conditional clauses. These chapters significantly expand the data coverage of the theory of A-quantification. Building on previous work of mine on exceptives, I analyze unless-clauses as exceptive operators on A-quantifiers. The analysis of only if-clauses, treated as conditional clauses that combine if with the focus adverb only, unearthes some interesting new properties. Chapter 6, finally, examines the phenomenon of donkey-anaphora in the light of the results of the previous chapters. I show that a solution to the proportion problem may become possible once we combine the situation-semantic approach to adverbial quantification with the pragmatic theory developed in Chapter 2 and further elaborated in the analysis of donkey anaphora in complex conditionals. (shrink)

Refinement geometry defines a directed subdivision structure over history-prefix spaces generated by admissible stability predicates. This paper analyzes the effective realizability of that structure within represented-space semantics. Stability predicates are formalized in uniformly semi-decidable witness form, yielding certified fact sets that evolve monotonically under refinement. A partitioning functional Pi maps finite-information access to a history into the corresponding directed family of refinement partitions. We prove that Pi is Type-2 computable: every finite portion of refinement structure depends on only finitely (...) many oracle interactions. Refinement asymmetry arises as a direct consequence of witness-based predicate semantics. Certified distinctions accumulate monotonically and are never revoked, establishing irreversibility at the level of refinement structure independent of dynamical assumptions. We further show that the canonical maximal partition induced by admissible predicates is computably generable through directed refinement of finite certification stages. Worlds, defined as blocks of the canonical maximal partition, therefore form a recursively enumerable set. Worldhood need not be decidable, and maximality is not finitely certifiable, yet every world arises through effective generation of finite refinement prefixes. In the effective setting, each refinement stage induces a computably presented equivalence relation on a countable domain of names, and branching corresponds to monotone contraction of indistinguishability rather than enlargement of the underlying history space. These results provide a computability-theoretic classification of refinement geometry, establishing constructive generation of maximal distinction structure under finite-information semantics and clarifying the effective consequences of stability-based refinement. (shrink)

The paper surveys the currently available axiomatizations of common belief (CB) and common knowledge (CK) by means of modal propositional logics. (Throughout, knowledge- whether individual or common- is defined as true belief.) Section 1 introduces the formal method of axiomatization followed by epistemic logicians, especially the syntax-semantics distinction, and the notion of a soundness and completeness theorem. Section 2 explains the syntactical concepts, while briefly discussing their motivations. Two standard semantic constructions, Kripke structures and neighbourhood structures, are introduced in (...) Sections 3 and 4, respectively. It is recalled that Aumann's partitional model of CK is a particular case of a definition in terms of Kripke structures. The paper also restates the well-known fact that Kripke structures can be regarded as particular cases of neighbourhood structures. Section 3 reviews the soundness and completeness theorems proved w.r.t. the former structures by Fagin, Halpern, Moses and Vardi, as well as related results by Lismont. Section 4 reviews the corresponding theorems derived w.r.t. the latter structures by Lismont and Mongin. A general conclusion of the paper is that the axiomatization of CB does not require as strong systems of individual belief as was originally thought- only monotonicity has thusfar proved indispensable. Section 5 explains another consequence of general relevance: despite the "infinitary" nature of CB, the axiom systems of this paper admit of effective decision procedures, i.e., they are decidable in the logician's sense. (shrink)

Roman Suszko said that “Obviously, any multiplication of logical values is a mad idea and, in fact, Łukasiewicz did not actualize it.” The aim of the present paper is to qualify this ‘obvious’ statement through a number of logical and philosophical writings by Professor Jan Woleński, all focusing on the nature of truth-values and their multiple uses in philosophy. It results in a reconstruction of such an abstract object, doing justice to what Suszko held a ‘mad’ project within a generalized (...) logic of judgments. Four main issues raised by Woleński will be considered to test the insightfulness of such generalized truth-values, namely: the principle of bivalence, the logic of scepticism, the coherence theory of truth, and nothingness. (shrink)

This paper presents Version 9 of Cognitional Mechanics as the final formulation prior to the abstraction of the operational layer into Operatiology. The subsequent framework, Principles of Operatiology: New Foundation of Cognitional Mechanics (DOI: 10.5281/zenodo.20350414), reformulates the minimal operational structure independently of any specific algebraic realization and establishes the abstract operational closure as the Tier-2 foundation of the framework. -------------------------------------------------------------------------------------- This paper establishes the foundational axiomatic framework of Cognitional Mechanics (Japanese: Chinou Rikigaku 知能力学)—a pure theoretical system that formalizes the structural (...) mechanisms inherent to intelligence through mathematical abstraction. Unlike conventional approaches rooted in physical dynamics or engineering implementations, Cognitional Mechanics constructs a self-contained theory based on three independent foundational axioms: (1) non-commutativity of semantic operations; (2) a complete ordered metric structure on semantic states, defined over an abstract totally ordered Abelian group D without presupposing the real numbers; and (3) a redundancy exclusion principle enforcing discriminative irreducibility. A fourth principle, the operational bound, is retained as Working Axiom 3 for notational continuity with the established corpus; it is a derived corollary of the three foundational axioms, as established by the Internal Language Theorem (DOI: 10.5281/zenodo.19350315). Version 6 introduced algebraic–geometric coupling connecting non-commutativity to geometric separation, formal set-theoretic definition of inaccessible domains, and the d-indistinguishability partition Π_d as the precise formulation of Axiom 4. Version 7 resolves three structural issues present in Version 6: Axiom 1 is strengthened to include the geometric persistence of non-commutative divergence under all subsequent operation sequences; the existence of non-trivial inaccessible domains is established as a theorem rather than a heuristic remark; and the derivation of Working Axiom 3 from the foundational triad is provided in full within this document (Appendix A), subsuming Corollary 5.9 of the Internal Language Theorem. By introducing a rigorous axiomatic structure—including a metric space of semantic states with defined distance functions satisfying non-negativity, symmetry, and triangle inequality—this framework transcends subjective interpretations of intelligence and establishes it as an object of formal inquiry. The theory absorbs conventional criticisms regarding measurability by positioning the operational limit c as an abstract logical boundary rather than a numerical constant, thereby maintaining theoretical self-containment without dependence on external observation or physical instantiation. Cognitional Mechanics provides a foundation for understanding intelligence-specific phenomena such as logical conflicts arising from non-commutative operation sequences, convergence and divergence in meaning formation, and the emergence of fundamentally unreachable semantic states. Version 8 establishes Cognitional Mechanics as the unique self-contained Tier-2 framework from which all formal structures are projected as Tier-3 outputs, without presupposing any of them: an a priori mathematology and The Theory of Foundation. Version 9 completes the uniqueness proof of the minimal operational structure C_min by introducing the canonical irreducible set I_{Π_d} and establishing via the Π_d-saturation condition (Axiom 2-(v)) that every admissible structure must contain all its elements. A formal Tier architecture (Tier-1: pre-formal structural necessity; Tier-2: closure-consistent operational structure; Tier-3: formal representational projection) is established in Appendix D, providing the structural foundation for Cognitional Mechanics as an a priori mathematology and The Theory of Foundation. Published ON May 16, 2026 DOI: 10.5281/zenodo.20226488. (shrink)

In the modular design of generative theory the syntax-semantics interface has accounted all along for meanings at the level of Logical Form. The syntax-pragmatics interface, on the other hand, is the result of what one may call the 'pragmatic turn' in the linguistic theory, where content is partitioned into given and new information. In other words, the structural division of the clause has been subjected to criteria of information, or discourse structure. Both interfaces require a structurally descriptive inventory whose (...) specific shapes can be motivated on theory-internal grounds only. The present collection of original articles develops the concept of these interfaces further. The papers in the first section focus on the syntax-semantics interface, those in the second section on the syntax-pragmatics interface. (shrink)

My 1981 paper Partition and Revision presented a premise semantics for counterfactuals that attributed their indeterminacy and context dependency to the many ways the facts of a world hang together - form 'lumps', that is. This paper is an investigation of lumping relations and their role in explaining certain puzzles of counterfactual reasoning. The version listed here is the 1989 version of the paper. My 2012 book 'Modals and Conditionals', chapter 5, has a thoroughly expanded and updated version. (...) Please consult and refer to the 2012 version when you want to cite this work. -/- Lumping relations rely on a semantics based on partial possible worlds or situations. A situation semantics opens up entirely new possibilities for the analysis of counterfactuals and has also led to progress in other areas of semantics, but it does so at a price. There are now many possible denotations for even the most basic logical words. Are there guidelines that help us pick the right ones? If there are several possible denotations for a given logical word, all equally plausible, do we find the expected ambiguities? About a third of the paper wrestles with those questions – primarily quantifiers and negation - before a framework is in place for the discussion of counterfactual reasoning proper in the rest of the paper. -/- . (shrink)

It has been recently argued that the well-known square of opposition is a gathering that can be reduced to a one-dimensional figure, an ordered line segment of positive and negative integers [3]. However, one-dimensionality leads to some difficulties once the structure of opposed terms extends to more complex sets. An alternative algebraic semantics is proposed to solve the problem of dimensionality in a systematic way, namely: partition (or bitstring) semantics. Finally, an alternative geometry yields a new and (...) unique pattern of oppositions that proceeds with colored diagrams and an increasing set of bitstrings. (shrink)

We shall describe the set of strongly meet irreducible logics in the lattice ϵLin.t of normal tense logics of weak orderings. Based on this description it is shown that all logics in ϵLin.t are independently axiomatizable. Then the description is used in order to investigate tense logics with respect to decidability, finite axiomatizability, axiomatization problems and completeness with respect to Kripke semantics. The main tool for the investigation is a translation of bimodal formulas into a language talking about partitions (...) of general frames into intervals so that relative to both Kripke frames and descriptive frames the expressive power of both languages coincides. (shrink)

This paper deals with structures ${\langle{\bf T}, I\rangle}$ in which T is a tree and I is a function assigning each moment a partition of the set of histories passing through it. The function I is called indistinguishability and generalizes the notion of undividedness. Belnap’s choices are particular indistinguishability functions. Structures ${\langle{\bf T}, I\rangle}$ provide a semantics for a language ${\mathcal{L}}$ with tense and modal operators. The first part of the paper investigates the set-theoretical properties of the set (...) of indistinguishability classes, which has a tree structure. The significant relations between this tree and T are established within a general theory of trees. The aim of second part is testing the expressive power of the language ${\mathcal{L}}$ . The natural environment for this kind of investigations is Belnap’s seeing to it that (stit). It will be proved that the hybrid extension of ${\mathcal{L}}$ (with a simultaneity operator) is suitable for expressing stit concepts in a purely temporal language. (shrink)

I show that speaker bias in _polarity focus questions_ (PFQs) is context sensitive, while speaker bias in _high negation questions_ (HNQs) is context insensitive. This leads me to develop separate accounts of speaker bias in each of these kinds of polar questions. I argue that PFQ bias derives from the fact that they are frequently used in conversational contexts in which an answer to the question has already been asserted by an interlocutor, thus expressing doubt about the prior assertion. This (...) derivation explains their context sensitivity, and the fact that similar bias arises from polar questions that lack polarity focus. I also provide novel evidence that the prejacents of HNQs lack negation, and thus only have an outer negation reading (see, e.g., Ladd in Papers from the seventeenth regional meeting of the Chicago Linguistic Society, vol. 17, pp. 164–171, 1981 ; Romero and Han in Linguistics and Philosophy 27(5):609–658, 2004 ; Krifka in Contrastiveness in information structure, alternatives and scalar implicatures, pp. 359–398, 2017 ; AnderBois in Questions in discourse, pp. 118–171, 2019 ; Frana and Rawlins in Semantics and Pragmatics 12(16):1–48, 2019 ; Jeong in Journal of Semantics 38(1):49–94, 2020 ). Based on a treatment of HNQs as denoting unbalanced partitions (Romero and Han in Linguistics and Philosophy 27(5):609–658, 2004 ), and competition with their positive polar question alternatives, I propose a novel derivation of speaker bias in HNQs as a conversational implicature. Roughly, if the speaker is ignorant, then a positive polar question will be more useful because it is more informative, so the use of an HNQ conveys that the speaker is not ignorant. The denotation of the HNQ then makes clear which way the speaker is biased. The result separates high negation from verum focus, and I argue that it is more parsimonious and has better empirical coverage than prior accounts. (shrink)

Branch Lengths and Word Trees. Word trees are one of the available tools in textual analysis to visualize semantic relationships between the words of a text. Tree construction methods from the co-occurrence distances between words in a text produce trees whose edge lengths are difficult to analyze. In order to make the visual interpretation of the tree easier, long edges should separate semantic classes of words. Therefore, cutting the longest edges in the tree should lead to a partition of (...) the word set with relevant classes. Using two corpuses where a subset of words was partitioned into semantic classes, we evaluate several formulas computing new edge lengths for a tree built from co-occurrence distances, aiming at making the interpretation of the tree easier and more reliable. (shrink)

In the human cognitive economy there are four grades of epistemic involvement. Knowledge partitions into distinct sorts, each in turn subject to gradations. This gives a fourwise partition on ignorance, which exhibits somewhat different coinstantiation possibilities. The elements of these partitions interact with one another in complex and sometimes cognitively fruitful ways. The first grade of knowledge I call “anselmian” to echo the famous declaration credo ut intelligam, that is, “I believe in order that I may come to know”. (...) As construed here, one knows in this anselmian way that E = mc2 just in case one knows that sentence expresses a true statement, but without having to understand the proposition it expresses. Most epistemologists ignore the significance of this grade of epistemic involvement. In a second grade of epistemic involvement, knowing that E = mc2 is knowing what that sentence means and understanding the proposition it express. This is knowledge in the propositional or semantic sense, and is the dominant target of epistemological investigation. Tacit and implicit knowledge occupies another tier. A typical example would be something that someone has “known all along” but, until now, hasn’t had occasion to put her mind to it or formulate in words. TI-knowledge remains a minority interest in today’s epistemology. Operating at a fourth grade of epistemic involvement is what I call “impact”-knowledge, which is the knowledge of a matter at its deepest and most widespread. An example, to be discussed below, is the knowledge that was generated by the Wiles proof of Fermat’s last theorem. Its true importance lies not only, or even mainly, in its verification of a commonly accepted fact about numbers, but rather in its enrichment of the mathematics of elliptical curves and the promise it holds for greater advancement into the mathematical unknown. Knowledge of this fourth grade has yet to find a seat in the parliaments of epistemology. Knowledge of the anselmian sort is independent of the other three. Tacit and implicit knowledge is incompatible with anselmian and semantic knowledge but coinstantiable with impact-knowledge. Semantic knowledge is incompatible with tacit and implicit knowledge but coinstantiable with the others. Impact-knowledge is pairwise coinstantiable with the others. Below I will bring the ignorance partitions into such alignment as they have with these ones. In doing so, I’ll propose a naturalized causal response epistemology designed to give these interactive distinctions the theoretical air they need to breathe. (shrink)

At conceptual and linguistic levels of cognition, events are said to be represented in terms of abstract categories, for example, the sentence Jackie cut the bagel with a knife encodes the categories Agent (i.e., Jackie) and Patient (i.e., the bagel). In this paper, we ask whether entities such as the knife are also represented in terms of such a category (often labeled “Instrument”) and, if so, whether this category has a prototype structure. We hypothesized the Proto-instrument is a tool: a (...) physical object manipulated by an intentional agent to affect a change in another individual or object. To test this, we asked speakers of English, Dutch, and German to complete an event description task and a sentence acceptability judgment task in which events were viewed with more or less prototypical instruments. We found broad similarities in how English, Dutch, and German partition the semantic space of instrumental events, suggesting there is a shared concept of the Instrument category. However, there was no evidence to support the specific hypothesis that tools are the core of the Instrument category—instead, our results suggest the most prototypical Instrument is the direct extension of an intentional agent. This paper supports theoretical frameworks where thematic roles are analyzed in terms of prototypes and suggests new avenues of research on how instrumental category structure differs across linguistic and conceptual domains. (shrink)

The main doctrines of the traditional logic of terms (logica termini) are standardly organized according to the formation structure of syllogistic inferences. A syllogistic inference is analyzed into propositions, and propositions, in the last instance, to terms; the logic of terms, in line with this formation structure, is partitioned into the doctrines, respectively, of terms (terminorum), of propositions (propositionum) or judgments (judiciorum), and of immediate and mediate inferences or followings (consequentiarum immediatarum/mediatarum). This structure communicates the idea that a given doctrine (...) could be treated, to a certain extent, independently of the next one to come, so that propositions, for instance, could be examined, at least to a certain extent, independently of syllogistic inferences. Some classical philosophers such as Immanuel Kant have developed approaches that break in part this order of analysis which finds its clearest expression in the Port-Royal logic (Arnauld & Nicole’s Logic or the Art of Thinking). In Kant’s case the order is changed in favor of the doctrine of judgements. This paper examines the French philosopher Jules Lachelier’s (1832-1918) approach which similarly breaks the same doctrinal order, and which, more specifically, refines the typification of propositions according to the roles to be played by propositions in syllogisms. What lies at the core of this approach is the identification of the semantic values of categorical propositions (or, as Lachelier calls them, of propositions of inherence) in terms of modal statuses which are to determine these roles. Lachelier seems to use the set of values he assigns to the categorical forms as a tool for testing logical implication among types of predication, that is, as some sort of semantic theory in the modern sense. Lachelier also discusses the three-figured categorical syllogistic along with a method, effectively used by G. W. Leibniz, of transforming syllogistic moods into each other, and tries to confirm his semantic theory in terms of such syllogistic. This paper explains Lachelier’s analysis of meaning by treating it as a non-formal semantics of predication, and tries to make some modern sense of Lachelier’s general approach to syllogistic. (shrink)