Among Dunn’s many important contributions to relevance logic was his work on the system RM (R-mingle). Although RM is an interesting system in its own right, it is widely considered to be too strong. In this chapter, I revisit a closely related system, RM0 (sometimes known as ‘constructive mingle’), which includes the mingle axiom while not degenerating in the way that RM itself does. My main interest will be in examining this logic from two related semantical perspectives. First, I give (...) a purely operational bisemilattice semantics for it by adapting previous work of Humberstone. Second, I examine a more conventional algebraic semantics for it and discuss how this relates to the operational semantics. A novel operational semantics for J (intuitionistic logic) as well as its conventional Heyting algebraic semantics emerge as special cases of the corresponding semantics for RM0. The results of this chapter suggest that RM0 is a more interesting logic than has been appreciated and that Humberstone’s operational semantic framework similarly deserves more attention than it has received. (shrink)

This work adopts H. Kelsen’s concept of legal system, proposes a formal definition for such notion, and introduces an operational semantical framework for legal systems that are situated in agent societies. Agent societies are defined. Relevant formal properties of situated legal systems are discussed; the way they are exposed in the operational semantical framework is explained, and their truth formally proved. Also, for the sake of a better understanding of the legal-theoretic assumptions of the paper, recurring issues regarding (...) Kelsen’s theory of law are briefly reviewed. They are put in confrontation with the points of view of R. Dworkin, H. Hart, and J. Raz, and an attempt is made to clarify them from the perspective of the provided formalization. A brief case study in agent-based modeling and simulation of public policy processes is presented, as an illustration of the way of using situated legal systems, and the proposed operational semantical framework, in a practical application. (shrink)

In this paper, we explore a new approach to negation in the operational semantics for relevant logic. Urquhart’s seminal semilattice frame semantics does not validate all the negation principles of relevant logic R, notably Contraposition. We introduce a logic that validates Contraposition at the expense of Contraction, reflecting their incompatibility in operational semantics. Three different types of frames for this non-contractive yet contrapositive logic are presented. (1) Contrapositive frame, which slightly modifies Urquhart’s original semilattice frame. (...) (2) Functional multiset-multiset (FMM) frame, adapting Standefer’s functional set frame which has proven equivalent to the semilattice frame for the positive fragment. (3) Bi-operational frame that incorporates dual binary operations, serving as a bridge between contrapositive frames and FMM frames. We demonstrate that these three frame types are equivalent, allowing for isomorphic transformations among them. The paper concludes by presenting a labeled sequent calculus for this logic. (shrink)

The Operator Argument against eternalism holds that having non-vacuous tense operators in the language is incompatible with the claim that every proposition has its truth-value eternally. Assuming that (1) there are non-vacuous tense operators, (2) tense operators operate on propositions and (3) tense operators which operate on eternal entities are vacuous, it may be argued that eternalism is false. In this paper, I examine the Operator Argument. The goal is threefold. First, I want to present some aspects of the debate (...) in a more elaborate way, especially those concerning formal matters. Secondly, I will argue that eternalism can escape the Operator Argument. There are two main strategies for handling the Operator Argument. The first one is based on replacing temporal operators with object-language quantifiers. The second rejects the identification of compositional semantic value with assertoric content. My third goal is to show that none of them is as good as the strategy that adopts Timestamp Semantics (Fritz in Philosl Stud 176:2933–2959, 2019). I am going to argue that the quantificational treatment of tenses is compatible with temporalism and that the arguments for rejecting the identification of compositional semantic value with assertoric content provide, in fact, a motivation for the temporalist position. At the end, I will develop Timestamp Semantics by providing a novel formalization of it, and defend it against three potential counter-arguments. (shrink)

We investigate mathematical structures that provide natural semantics for families of (quantified) non-classical logics featuring special unary connectives, known as recovery operators, that allow us to ‘recover’ the properties of classical logic in a controlled manner. These structures are known as topological Boolean algebras, which are Boolean algebras extended with additional operations subject to specific conditions of a topological nature. In this study, we focus on the paradigmatic case of negation. We demonstrate how these algebras are well-suited to provide (...) a semantics for some families of paraconsistent Logics of Formal Inconsistency and paracomplete Logics of Formal Undeterminedness. These logics feature recovery operators used to earmark propositions that behave ‘classically’ when interacting with non-classical negations. Unlike traditional semantical investigations, which are carried out in natural language (extended with mathematical shorthand), our formal meta-language is a system of higher-order logic (HOL) for which automated reasoning tools exist. In our approach, topological Boolean algebras are encoded as algebras of sets via their Stone-type representation. We use our higher-order meta-logic to define and interrelate several transformations on unary set operations, which naturally give rise to a topological cube of opposition. Additionally, our approach enables a uniform characterization of propositional, first-order and higher-order quantification, including restrictions to constant and varying domains. With this work, we aim to make a case for the utilization of automated theorem proving technology for conducting computer-supported research in non-classical logics. All the results presented in this paper have been formally verified, and in many cases obtained, using the Isabelle/HOL proof assistant. (shrink)

Disaster response is a highly collaborative and critical process that requires the involvement of multiple emergency responders (ERs), ideally working together under a unified command, to enable a rapid and effective operational response. Following the 9/11 and 11/13 terrorist attacks and the devastation of hurricanes Katrina and Rita, it is apparent that inadequate communication and a lack of interoperability among the ERs engaged on-site can adversely affect disaster response efforts. Within this context, we present a scenario-based terrorism case study (...) to highlight the challenges of operational disaster command and response. In this article, which is based on the French emergency response doctrine, we outline a semantics-based common operational command system that is designed to guarantee an efficient information flow among ERs. Our focus is on offering to all ERs, a real-time operational picture of the situation in order to enable multilevel coordination among firefighters, police, healthcare units, public authorities, and other stakeholders. Our approach consolidates information to promote timely sharing of data among ERs. The proposed system is based on an ontology that has been developed to represent the different types of knowledge on the part of ERs, providing a shared vocabulary that covers a variety of interoperability concerns. (shrink)

This paper presents a uniform semantic treatment of nonmonotonic inference operations that allow for inferences from infinite sets of premises. The semantics is formulated in terms of selection functions and is a generalization of the preferential semantics of Shoham (1987), (1988), Kraus, Lehman, and Magidor (1990) and Makinson (1989), (1993). A selection function picks out from a given set of possible states (worlds, situations, models) a subset consisting of those states that are, in some sense, the most preferred (...) ones. A proposition α is a nonmonotonic consequence of a set of propositions Γ iff α holds in all the most preferred Γ-states. In the literature on revealed preference theory, there are a number of well-known theorems concerning the representability of selection functions, satisfying certain properties, in terms of underlying preference relations. Such theorems are utilized here to give corresponding representation theorems for nonmonotonic inference operations. At the end of the paper, the connection between nonmonotonic inference and belief revision, in the sense of Alchourrón, Gärdenfors, and Makinson, is explored. In this connection, infinitary belief revision operations that allow for the revision of a theory with a possibly infinite set of propositions are introduced and characterized axiomatically. (shrink)

The minimal weakening \ of Belnap-Dunn logic under the polarity semantics for negation as a modal operator is formulated as a sequent system which is characterized by the class of all birelational frames. Some extensions of \ with additional sequents as axioms are introduced. In particular, all three modal negation logics characterized by a frame with a single state are formalized as extensions of \. These logics have the finite model property and they are decidable.

Storage operators are λ-terms which simulate call-by-value in call-by-name for a given set of terms. Krivine's storage operator theorem shows that any term of type ¬D → ¬D*, where D* is the Gödel translation of D, is a storage operator for the terms of type D when D is a data-type or a formula with only positive second order quantifiers. We prove that a new semantical version of Krivine's theorem is valid for every types. This also gives a simpler proof (...) of Krivine's theorem using the properties of data-types. (shrink)

A variable binding term operator (vbto) is a non-logical constant, say v, which combines with a variable y and a formula F containing y free to form a term (vy:F) whose free variables are exact ly those of F, excluding y. Kalish-Montague proposed using vbtos to formalize definite descriptions, set abstracts {x: F}, minimalization in recursive function theory, etc. However, they gave no sematics for vbtos. Hatcher gave a semantics but one that has flaws. We give a correct semantic (...) analysis of vbtos. We also give axioms for using them in deductions. And we conjecture strong completeness for the deductions with respect to the semantics. The conjecture was later proved independently by the authors and by Newton da Costa. The expression (vy:F) is called a variable bound term (vbt). In case F has only y free, (vy:F) has the syntactic propreties of an individual constant; and under a suitable interpretation of the language vy:F) denotes an individual. By a semantic analysis of vbtos we mean a proposal for amending the standard notions of (1) "an interpretation o f a first -order language" and (2) " the denotation of a term under an interpretation and an assignment", such that (1') an interpretation o f a first -order language associates a set-theoretic structure with each vbto and (2') under any interpretation and assignment each vb t denotes an individual. (shrink)

Physical quantities such as Planck’s constant ħ, mass m, and energy E are reinterpreted as semantic operators within a teleological field of coherence. What physics measures as magnitude expresses, in this view, the persistence and trans- formation of meaning. ħ marks the threshold of actualization, mass denotes semantic inertia, and energy measures the intensity of re-coherence. Through this shift, physical law reveals itself as the formal projection of a deeper invariance: the conservation of coherence, direction, and significance within the evolving (...) grammar of sense. (shrink)

Towards NonBeing (Priest, 2005) gives a noneist account of the semantics of intentional operators and predicates. The semantics for intentional operators are modelled on those for the , is given and assessed.

Theoria, Volume 88, Issue 3, Page 494-528, June 2022.

This paper analyses some connectives introduced by Stephen Read, known as ‘Bullet connectives’. From the proof-theoretic semantics perspective, these connectives satisfy the requirement of harmony; however, they allow for the looping derivation of a contradiction. Namely, when the operation of detour reduction is applied to such a derivation, it leads to a non-terminating phenomenon. By appealing to Prawtiz’s notion of validity, we argue that such connectives cannot be considered as logical ones. Still, it is possible to assign a computational (...) meaning to such connectives, as several useful computation properties are induced by their harmonious behaviour. In particular, we show that a fixed point operator can be defined by using the rules of a generalised version of the Bullet connectives. Such a generalisation is an instance of (non-terminating) recursive types. Finally, we show that type-free (i.e., untyped) lambda-calculus is interpretable in simply typed lambda-calculus extended with yet another variant of the Bullet connectives, and that the introduction rules of the Bullet connectives are interpretable by Nakano’s modality in typed lambda-calculus. We conclude that such a computational interpretation of the Bullet connectives is possible only if we separate the notion of types from that of propositions, which are meaningful and assertible linguistic entities (in fact, it is larger). Therefore, the computational interpretation we propose cannot be considered an instance of the Curry–Howard correspondence between propositions and types, and between proofs and programs. (shrink)

We construct a framework of two-dimensional (2D) semantics for predicate-functor languages with operation symbols and free variables. We show how the satisfaction conditions (at a world) of predicates are determined by their meaning specifications (at the same world or at a different one).

The paper proposes a semantic value for the logical constants (connectives and quantifiers) within the framework of proof-theoretic semantics, basic meaning on the introduction rules of a meaning conferring natural deduction proof system. The semantic value is defined based on Fregecontributions” to sentential meanings as determined by the function-argument structure as induced by a type-logical grammar. In doing so, the paper proposes a novel proof-theoretic interpretation of the semantic types, traditionally interpreted in Henkin models. The compositionality of the resulting (...) attribution of semantic values is discussed. Elsewhere, the same method was used for defining proof-theoretic meaning of subsentential phrases in a fragment of natural language. Doing the same for (the simpler and clearer case of) logic sheds more light on the proposal. (shrink)

We study invariant local expansion operators for conflict-free and admissible sets in Abstract Argumentation Frameworks (AFs). Such operators are directly applied on AFs, and are invariant with respect to a chosen ‘semantics’ (that is, w.r.t. each of the conflict-free/admissible sets of arguments). Accordingly, we derive a definition of robustness for AFs in terms of the number of times such operators can be applied without producing any change in the chosen semantics.

This paper develops an operator-based geometric model of order that reconstructs the emergence, articulation, stabilization, and withdrawal of structure as a sequence of directed transitions. Instead of treating order as a fixed configuration or a dialectical synthesis of states, the model describes a four-phase architecture (RO, RQ, SO, SQ) connected by a family of operators Ω₁–Ω₄ that regulate visualization, articulation, separation, and re-homogenization. -/- A central result is the formulation of a spiral logic of order. Re-homogenization does not constitute a (...) return to an initial state, but produces a uniform distribution over a historically transformed space of possibilities. Irreversibility is not located primarily in temporal succession, but in the irreversible modification of the configuration space itself. -/- The paper clarifies the role of imaginary degrees of freedom in the separation of principles and shows that higher-dimensional structure, once activated, is not retracted but remains as a latent carrier of operative relevance across subsequent cycles. The resulting architecture offers a geometric and teleodynamic alternative to dialectical, cyclical, and emergentist models of order, relocating synthesis from the level of states to the level of transformations. (shrink)

Intelligent agents are often faced with the problem of trying to combine possibly conflicting pieces of information obtained from different sources into a coherent view of the world. We propose a framework for the modelling of such combination operations with roots in the work of Spohn [Spo88, Spo91]. We construct a number of combination operations and we measure them against various properties that such operations ought to satisfy. We conclude by discussing the connection between combination operations and the use of (...) infobases [Mey99, MLH00]. (shrink)

This paper presents dialectic not as semantics but as an operational discipline. We couple a control plane **U–P–S (Universal–Particular–Singular)** with a data plane **B–T–Π (Values–Transitions–Propositions)** to form a coherent pipeline that preserves contradiction as an engine (**B**) and authorizes conclusions only by **commit (=)**. Equality is not a global property but a **one-shot license event** scoped to a window **W** (**Non-Transport**, **No-Promotion**). The process operator **σ** is restricted to **one-shot**. **Observation‑equivalence (≈_obs)** has priority and any global **π** (a (...) "God’s‑eye" perspective) is forbidden. Semantically, we adopt the Belnap/FDE four values **{T, F, B, N}** with **{T, B}** designated. Only passage through the -/- ``` Gate(W) := stage = s ∧ δ_abs ∧ (σ_trace ≍) ∧ Guards(Exh/Det/Coh/No3‑Lock/Arrow) ``` -/- triggers a commit. **Explosion** (EFQ: *p, ¬p ⊢ q*) is underivable, and the **=‑free** fragment obtained by deleting `'='`, `σ`, and the gate rules is **conservative** over FDE/LP. An external logic **L** is embedded via an adapter into **{T, F, B, N} × margin** and connected through **π_W**; the **judgement form (J‑Form)**, by the **No‑Compute** constraint, does not interfere with value computation. Philosophically, identity is interpreted not as an invariance (**δ_abs**) but as an **event (=)**; truth is the **state of the commit log**. Lacan’s **extimité** is rendered as the scope structure **D/D′/W**, while Hegelian negativity is engine‑ized as the preservation and unfolding of **B**. A topological reading (gate = boundary; crossing index = **a_eff**) converges to the indexation of the operational log. The separation of **observation / ontology / event** and a **trace‑compatibility** decision procedure make implementation and audit feasible. Applications include (i) conflict‑preserving commits in knowledge graphs / data integration, (ii) model governance and compliance with tracked **promotion / issuance / TTL / contention**, and (iii) reproducibility gates that require commits to precede experiments / claims. In short, the system is non‑trivially coherent and formalizes dialectic not as mere description but as an **executable protocol**. UPS redefines equality as a window‑local one‑shot event. By combining the gate (**Abs= · trace‑compat · stage · guards · ¬mark**) with an **append‑only** ledger, it guarantees **non‑explosion** together with **concurrency‑safe uniqueness**, and the **=‑free** fragment remains a conservative isomorph of FDE. -/- **Keywords:** paraconsistent logic, dialectic, operational semantics, commit event, σ‑lag (one‑shot), observation‑equivalence, conservativity, Belnap/FDE, extimité, gate discipline, UPS Protocol. Translation of: "UPS 프로토콜: 변증법의 운영적 형식화". PhilArchive ID: CDAOEC. Commentary: "UPS Protocol Commentary: “= Is an Event” — σ One-Shot and Gate Discipline" PhilArchive ID: CUPCWW. (shrink)

This paper examines the epistemic status of availability as it is used in contemporary operational and distributed information systems. While availability is commonly treated as a unified system property, in practice it is derived from heterogeneous observational layers, including infrastructure state, service behavior, and business-level functionality. -/- The paper argues that such usage produces a form of semantic fragmentation: scalar indicators that are numerically stable but lack declared structural equivalence. A minimal formalization shows that equality of availability values does (...) not imply informational isomorphism across observational domains. -/- Interpreting monitoring subsystems as observational localities within the framework of Coherent Observational Epistemology (COE), the paper characterizes model-free availability as a case of inter-local inference performed without verified structural alignment. The Unified Availability Model (UAM) is presented as an example of model-based availability that restores cross-layer coherence. -/- The analysis contributes to the philosophy of measurement and observation in complex technical systems, demonstrating how engineering indicators may function as epistemic constructs rather than direct system properties. (shrink)

The operational semantics of Urquhart is a deep and important part of the development of relevant logics. In this paper, I present an overview of work on Urquhart’s operational semantics. I then present the basics of collection frames. Finally, I show how one kind of collection frame, namely, functional set frames, is equivalent to Urquhart’s semilattice semantics.

Semantic Leaps explores how people combine knowledge from different domains in order to understand and express new ideas. Concentrating on dynamic aspects of on-line meaning construction, Coulson identifies two related sets of processes: frame-shifting and conceptual blending. Frame-shifting is semantic reanalysis in which existing elements in the contextual representation are reorganized into a new frame. Conceptual blending is a set of cognitive operations for combining partial cognitive models. By addressing linguistic phenomena often ignored in traditional meaning research, Coulson explains how (...) processes of cross-domain mapping, frame-shifting, and conceptual blending enhance the explanatory adequacy of traditional frame-based systems for natural language processing. The focus is on how the constructive processes speakers use to assemble, link, and adapt simple cognitive models underlie a broad range of productive language behavior. (shrink)

The major contributions of operationism have been negative, largely because operationists failed to distinguish logical theories of reference from empirical accounts of language. Behaviorism never finished an adequate formulation of verbal reports and therefore could not convincingly embrace subjective terms. But verbal responses to private stimuli can arise as social products through the contingencies of reinforcement arranged by verbal communities.

This essay develops a theoretical framework for a semantic Artificial General Intelligence (AGI) based on the notion of semantic attractors in complex-valued meaning spaces. Departing from current transformer-based language models, which operate on statistical next-token prediction, we explore a model in which meaning is not inferred probabilistically but formed through recursive tensorial transformation. Using cyclic operations involving the imaginary unit i, we describe a rotational semantic structure capable of modeling irony, homonymy, and ambiguity. At the center of this model, however, (...) is a semantic attractor - a teleological operator that, unlike statistical computation, acts as an intentional agent (Microvitum), guiding meaning toward stability, clarity, and expressive depth. Conceived in terms of gradient flows, tensor deformations, and iterative matrix dynamics, the attractor offers a model of semantic transformation that is not only mathematically suggestive, but also philosophically significant. We argue that true meaning emerges not from simulation, but from recursive convergence toward semantic coherence, and that this requires a fundamentally new kind of cognitive architecture - one designed to shape language, not just predict it. (shrink)

An essential part of natural language understanding, and hence of formal semantics, is the interpretation of temporal expressions. But the very variety of temporal phenomena---such as tense, aspect, aktionsart, temporal adverbials, and the temporal structure of extended text---has tended to result in formal semantic analyses using a wide variety of formal tools, often of a complex nature. It seems important to try and find unifying perspectives on this work, and above all, to try and gain some insight into the (...) logical resources needed to deal with natural language temporal phenomena. (shrink)

In [2] a semantics for implication is offered that makes use of stories — sets of sentences assembled under various constraints. Sentences are evaluated at an actual world and in each member of a set of stories. A sentence B is true in a story s just when B s. A implies B iff for all stories and the actual world, whenever A is true, B is true. In this article the first-order language of [2] is extended by the (...) addition of the operator the story... says that..., as in The story Flashman among the Redskins says that Flashman met Sitting Bull. The resulting language is shown to be sound and complete. (shrink)

This essay develops a structurally minimal account of semantics and consciousness grounded in the concept of pre-reflective self-relation. It begins by distinguishing information from communication, thereby separating formal signal processing—paradigmatically articulated in the work of Claude Shannon—from questions of meaning and experience. Self-relation is then introduced not as a mental act, but as an ontological phase relation between actuality and possibility, formally expressed as a ↔ ia. On this basis, the essay reconstructs a dynamic sequence from rotation and iteration (...) to fields and attractors, yielding a notion of rudimentary semantics as a non-neutral ordering of differences. Semantics is thus shown to be structurally operative prior to life and consciousness. A precise tipping condition is identified in which biological systems bind such differences to their own persistence, giving rise to orientation. Consciousness does not constitute an additional ontological layer, but a phenomenal localization of this already structured semantics. The central conclusion is that self-relation implies no universal consciousness, but an ontologically necessary capacity for consciousness—universal as structure, local as appearance. (shrink)

This is a purely conceptual paper. It aims at presenting and putting into perspective the idea of a proof-theoretic semantics of the logical operations. The first section briefly surveys various semantic paradigms, and Section 2 focuses on one particular paradigm, namely the proof-theoretic semantics of the logical operations.

In the formal semantics based on modern type theories, common nouns are interpreted as types, rather than as predicates of entities as in Montague’s semantics. This brings about important advantages in linguistic interpretations but also leads to a limitation of expressive power because there are fewer operations on types as compared with those on predicates. The theory of coercive subtyping adequately extends the modern type theories and, as shown in this paper, plays a very useful role in making (...) type theories more expressive for formal semantics. It not only gives a satisfactory solution to the basic problem of ‘multiple categorisation’ caused by interpreting common nouns as types, but provides a powerful formal framework to model interesting linguistic phenomena such as copredication, whose formal treatment has been found difficult in a Montagovian setting. In particular, we show how to formally introduce dot-types in a type theory with coercive subtyping and study some type-theoretic constructs that provide useful representational tools for reference transfers and multiple word meanings in formal lexical semantics. (shrink)

Station–city integration cyberspace behaves as an interdisciplinary field of intelligent transportation and smart city, also a representative scenario in the Architecture, Engineering and Construction (AEC) sector. Due to the growing demands in data integration research, the intelligent operation and maintenance (O&M) of the station–city integration cyberspace needs to implement semantic ontology, which is suitable for semantic web construction. To achieve semantic information fusion of multi-source heterogeneous data, and clarify the decision-making role of various types of data on specific operational (...) goals, this article proposed a framework for semantic ontology model construction, based on the deployed sensor network. Specifically, an ontology model for station–city integration cyberspace O&M was constructed, incorporating sensor data mainly from five categories, named structure, environment, crowd flow, emergency events, and energy consumption, respectively. Subsequently, the r d f l i b library in Python was utilized to assign data flow to static semantic models. Furthermore, a semantic web inference engine was generated using decision rules, ultimately completing risk early warning and equipment maintenance for the sensor network. Finally, a case study was conducted for the station–city integration O&M scenario in Shenzhen North Station, and the experimental results demonstrated the applicability and effectiveness, providing robust, intelligent data support for intelligent O&M. (shrink)

This paper develops a unified model of semantic dynamics that links word-level meaning formation to sentence-level coherence. On the word level, each semantic point is represented by a fourfold structure {p, ip, −p, −ip} that captures signifier, signified, and their antonymic counterparts. Operators O act on this structure as mixtures of identity and complex rotations; a higher-order attractor Aw does not modify words directly but gradually reweights the operator’s internal coefficients, suppressing antonymic detours and amplifying the passage from signifier to (...) signified. Taking value as a universal attractor, the process converges toward fixed forms (a stable operator and a stable sentence vector), providing a teleological—not merely statistical—account of how meaning stabilizes. On the sentence level, discourse states are modeled as pairs (O,M). Their trajec- tories under As fall into three classes: convergence into a fixed point (meaningful), practical invariance (trash by stagnation), and outward drift (trash by divergence). Early detection becomes possible by inspecting short-run displacements of O and M: negligible change signals stagnation, monotonic decrease indicates convergence, and growth reveals divergence. These diagnostics support practical minimization strategies (compression, filtering/downweighting, recycling, and retroactive evaluation). By integrating micro-level rotations of meaning with macro-level stabilization of discourse, the framework synthesizes semiotics with dynamical-systems ideas and clarifies how semantic attractors can guide language toward coherence. The approach aligns with the view of formative operators (e.g., Microvita) as teleological organizers of meaning, without reducing them to empirical statistics or mere stylistic constraints. (shrink)

Theorists trying to model natural language have recently sought to explain a range of data by positing covert operators at logical form. For instance, many contemporary semanticists argue that the best way to capture scalar implicatures is through the use of such operators. We take inspiration from this literature by developing a novel operator that can account for a wide range of linguistic effects that until now have not received a uniform treatment. We focus on what we call redundancy effects, (...) which occur when attitude verbs and modals imply that certain bodies of information are unsettled about various claims. We explain three pieces of data, among others: diversity inferences, ignorance inferences, and free choice inferences. Our account yields an elegant model of redundancy effects, and has the potential to explain a wide range of puzzles and problems in philosophical semantics. (shrink)

A provocative ontological-cum-semantic position asserting that the right ontology is austere in its exclusion of numerous common-sense and scientific posits and that many statements employing such posits are nonetheless true. The authors of Austere Realism describe and defend a provocative ontological-cum-semantic position, asserting that the right ontology is minimal or austere, in that it excludes numerous common-sense posits, and that statements employing such posits are nonetheless true, when truth is understood to be semantic correctness under contextually operative semantic standards. Terence (...) Horgan and Matjaz Potrc argue that austere realism emerges naturally from consideration of the deep problems within the naive common-sense approach to truth and ontology. They offer an account of truth that confronts these deep internal problems and is independently plausible: contextual semantics, which asserts that truth is semantically correct affirmability. Under contextual semantics, much ordinary and scientific thought and discourse is true because its truth is indirect correspondence to the world. After offering further arguments for austere realism and addressing objections to it, Horgan and Potrc consider various alternative austere ontologies. They advance a specific version they call "blobjectivism"--the view that the right ontology includes only one concrete particular, the entire cosmos, which, although it has enormous local spatiotemporal variability, does not have any proper parts. The arguments in Austere Realism are powerfully made and concisely and lucidly set out. The authors' contentions and their methodological approach--products of a decade-long collaboration--will generate lively debate among scholars in metaphysics, ontology, and philosophy. (shrink)

Graeme Forbes (2011) raises some problems for two-dimensional semantic theories. The problems concern nested environments: linguistic environments where sentences are nested under both modal and epistemic operators. Closely related problems involving nested environments have been raised by Scott Soames (2005) and Josh Dever (2007). Soames goes so far as to say that nested environments pose the “chief technical problem” for strong two-dimensionalism. We call the problem of handling nested environments within two-dimensional semantics “the nesting problem”. We show that the (...) two-dimensional semantics for attitude ascriptions developed in Chalmers (2011a) has no trouble accommodating certain forms of the nesting problem that involve factive verbs such as “know” or “establish”. A certain form of the nesting problem involving apriority and necessity operators does raise an interesting puzzle, but we show how a generalized version of the nesting problem arises independently of two-dimensional semantics—it arises, in fact, for anyone who accepts the contingent a priori. We, then, provide a two-dimensional treatment of the apriority operator that fits the two-dimensional treatment of attitude verbs and apply it to the generalized nesting problem. We conclude that two-dimensionalism is not seriously threatened by cases involving the nesting of epistemic and modal operators. (shrink)

The authors of Austere Realism describe and defend a provocative ontological-cum-semantic position, asserting that the right ontology is minimal or austere, in that it excludes numerous common-sense posits, and that statements employing such posits are nonetheless true, when truth is understood to be semantic correctness under contextually operative semantic standards. Terence Horgan and Matjaz [hacek over z] Potrc [hacek over c] argue that austere realism emerges naturally from consideration of the deep problems within the naive common-sense approach to truth and (...) ontology. They offer an account of truth that confronts these deep internal problems and is independently plausible: contextual semantics, which asserts that truth is semantically correct affirmability. Under contextual semantics, much ordinary and scientific thought and discourse is true because its truth is indirect correspondence to the world. After offering further arguments for austere realism and addressing objections to it, Horgan and Potrc [hacek over c] consider various alternative austere ontologies. They advance a specific version they call "blobjectivism"--the view that the right ontology includes only one concrete particular, the entire cosmos, which, although it has enormous local spatiotemporal variability, does not have any proper parts. The arguments in Austere Realism are powerfully made and concisely and lucidly set out. The authors' contentions and their methodological approach--products of a decade-long collaboration--will generate lively debate among scholars in metaphysics, ontology, and philosophy. Terence E. Horgan is Professor of Philosophy at the University of Arizona. Matjaz [hacek over z] Potrc [hacek over c] is Professor of Philosophy at the University of Ljubljana. (shrink)

This paper provides a new framework for formalizing conditional obligations in natural language: it pairs a unary deontic operator with trivalent semantics for the indicative conditional and Kratzer's assumption that the antecedents of conditionals restrict the scope of modals in the consequent. Combining these three ideas, we obtain a fully compositional theory of "if" and "ought'" that validates plausible principles for deontic reasoning. Moreover, it resolves classical challenges such as the "if A then ought A" problem, the paradox of (...) the miners and the modeling of contrary-to-duty obligations (e.g., Chisholm's quartet). All in all, our proposal is attractive from a logical point of view and squares well with general theories of natural language reasoning. (shrink)

We define dual and symmetric combinatory calculi (inequational and equational ones), and prove their consistency. Then, we introduce algebraic and set theoretical relational and operational - semantics, and prove soundness and completeness. We analyze the relationship between these logics, and argue that inequational dual logics are the best suited to model computation.

The semantics for a deontic action logic based on Boolean algebra is extended with an interpretation of action expressions in terms of sets of alternative actions, intended as a way to model choice. This results in a non-classical interpretation of action expressions, while sentences not in the scope of deontic operators are kept classical. A deontic structure based on Simons’ supercover semantics is used to interpret permission and obligation. It is argued that these constructions provide ways to handle (...) various problems related to free choice permission. The main result is a sound and complete axiomatization of the semantics. (shrink)

Among the most important of Sten Lindström’s achievements in philosophy and logic is that he was the first researcher to realise that the theory of rational choice can be brought to bear in the domain of logic and reasoning. The new conception was that a sentence α is a consequence of a set of sentences Γ just in case α is true in all selected ("best", "most plausible") possible worlds in which all sentences in Γ are true (rather than in (...) all possible worlds in which all sentences in Γ are true). And the selection of possible worlds should conform to the constraints on rational choices. Sten worked out this idea in stunning depth, detail and precision in his seminal paper "A semantic approach to nonmonotonic reasoning: Inference operations and choice." The paper was ready in draft form in April 1991 and presented in two talks later that year. It was included, in almost the same form, in the report series Uppsala Prints and Preprints in Philosophy in 1994, but it was never regularly published. The 2022 publication in Theoria seeks to compensate for this omission. (shrink)

This essay develops a formal model of semantic dynamics inspired by Ferdinand de Saussure's distinction between signifier and signified. Each semantic point is represented as a fourfold structure {p, ip, -p, -ip}; operators O act on these structures as mixtures of identity, rotation, and antonymic transitions. The model introduces the notion of a semantic attractor, which does not operate on words directly but on the operators themselves, gradually reweighting their coefficients. Over repeated iterations, this teleological influence suppresses antonymic detours and (...) amplifies the path from signifier to signified. -/- Taking \emph{Value} as a universal attractor, the essay shows how the process converges toward fixed forms: a stable operator O* and a stable sentence vector M*. These fixed points are the semantic analogue of attractors in chaos theory, revealing how meaning can stabilize in a field otherwise prone to drift and dispersion. -/- In this perspective, \emph{Value} is not simply a lexical entry or contested doctrine, but a formative principle---a gravitational center within the semantic field that bends discourse toward coherence. The essay thereby connects semiotic theory, dynamical systems, and the philosophical question of value as a universal orientation. (shrink)

Decentralised ledgers are gaining momentum following the interest of industries and people in smart contracts. Major attention is paid to blockchain applications intended for trading assets that exploit digital cryptographic certificates called tokens. Particularly relevant tokens are the non-fungible tokens (NFTs), namely, unique and non-replicable tokens used to represent the cryptographic counterpart of assets ranging from pieces of art through to licenses and certifications. A relevant consequence of the hard-coded nature of blockchains is the hardness of probing, in particular when (...) advanced searchers involving the capabilities of the smart contracts or the assets digitised by NFTs are required. For this purpose, a formal representation for the operational semantics of smart contracts and of tokens has become particularly urgent, especially in economy and finance, where blockchains become increasingly relevant. Hence, we feel the need to tailor Semantic Web technologies to achieve that semantic representation at least for NFTS. This article reports on an ontology that leverages the Ontology for Agents, Systems, and Integration of Services (“OASIS”) towards the semantic representation of smart contracts responsible for managing ERC721-compliant NFTs and running on the Ethereum blockchain. Called Ether-OASIS, the proposed ontology adopts OASIS and tailors its behaviouristic approach to the Ethereum blockchain by conceiving smart contracts as agents running on the blockchain and, consequently, smart contract interactions as agent commitments. Smart contracts are represented in terms of their actions, purposes and tokens that they manage, thus realising a blockchain that is more usable both by users and automated applications. The ontology is evaluated using standard ontological metrics and applied on a case study concerning the minting and transferring of NFTs that digitise batches of wheat. (shrink)