In this paper, we generalize the soft set to the hypersoft set by transforming the function F into a multi-attribute function. Then we introduce the hybrids of Crisp, Fuzzy, Intuitionistic Fuzzy, Neutrosophic, and Plithogenic Hypersoft Set.

0. Introductory remarks. I assume that every serious theory of language must give some explicit account of the relationship between expressions in the language described and expressions in some interpreted language which spells out the semantics of the language.1 Let's call this relationship the translation relation. Theories differ as to how this relation is specified. In the Aspects theory of syntax, taken together with a Katz-Postal view of "semantic rules", it was assumed that the relation was defined on deep structures. (...) Serious problems led to modifications of this view in several directions. Chomsky's latest papers assume that a modified 'intermediate structure' is transformed by rules of interpretation to a level of representation called 'logical form'. Common to all of these approaches is the assumption that the translation rules are defined initially on syntactic structures of one sort or another. Let us call this assumption the configurational hypothesis: the translation rules all have the form: [183]. (shrink)

My philosophico-poetrical system is not all my own. I built upon Valéry's remark: "To write regular verses destroys... an infinite number of fine possibilities but at the same time it suggests a multitude of distant and unexpected thoughts." The problem with pursuing the project and allowing for metaphor is that one starts with a line and searches for a line that rhymes and chooses a line with a metaphor in it which expresses common thoughts. By banning metaphor, one increases the (...) chances of distant and unexpected thoughts figuring the rhyme. (I think the AI has cut my remark "That's not how I interpret the lyrics."). (shrink)

Institute of Theoretical Astronomy, University of Cambridge, Cambridge, UK 3fS. received 28th August 1970, in final revised form 1st July 1971..

In this paper we extend Wittgenstein’s notion of family resemblance to translation, interpretation, and comparison across traditions. There is no need for universals. This holds for everyday concepts such as green and qing 青, philosophical concepts such as emotion(s) and qing 情, as well as philosophical categories such as form(s) of life and dao 道. These notions as well as all other concepts from whatever tradition are family resemblance concepts. We introduce the notion of quasi-universal, which connects family resemblance concepts (...) from a limited number of traditions. The possibility and necessity of extending family resemblance concepts across traditions dissolves the false antinomy of universalism versus relativism. (shrink)

We prove the determinacy of all Δ 1 1 games on arbitrary trees, and we use this result and the assumption that a measurable cardinal exists to demonstrate the determinacy of all games on ω ω that belong both to – Π 1 1 and to its dual.

My philosophico-poetical system has at its foundation Paul Valéry’s claim, “To write regular verses… destroys an infinite number of fine possibilities but at the same time it suggests a multitude of distant and unexpected thoughts.” Now someone might say, "Regular verses is a very old-fashioned kind of poetry. A lot of poetry today and for decades is free verse." But my system can lead to an appreciation of some contemporary poetic projects and even undermine this dichotomy of old-fashioned rhyme versus (...) contemporary poetry. First let me share some experience. I read some poetry at Manchester Central Library in late November 2024. It was free verse. After me, a woman performed some one vowel poetry: poetry in which you only use one vowel (and as many consonants as you like; you can use the vowel again and again by the way) - this poet used "u"! Hers significantly eclipsed my effort, I felt. I told a young comedian and poet about what happened and he said, "This one vowel poetry is a mere technical achievement," or words to that effect. My starting point for defining a technical achievement is that persons A and B have the same basic idea (or emotion) but A shows high craftsmanship skill in achieving the goal of expressing or communicating or realizing the idea - then you say that this is a technical achievement by A. I am not sure how to apply this starting point to one vowel poetry, but this is how I see it (I didn't tell the comedian-poet at the time): one vowel poetry is like rhyme. The rhyming poet writes a line and then they may want to say one thing in the next line, but that doesn't rhyme, so other thoughts occur to them in search of a rhyme. Similarly, the univocalic poet is forced by the demand to use only one vowel in strange directions. And these new directions of thought (or emotion) are of value. (shrink)

We show that if $$ satisfies the first-order Zermelo–Fraenkel axioms of set theory when the membership relation is ${ \in _1}$ and also when the membership relation is ${ \in _2}$, and in both cases the formulas are allowed to contain both ${ \in _1}$ and ${ \in _2}$, then $\left \cong \left$, and the isomorphism is definable in $$. This extends Zermelo’s 1930 theorem in [6].

We introduce a probabilistic extension of propositional intuitionistic logic. The logic allows making statements such as P≥sα, with the intended meaning “the probability of truthfulness of α is at least s”. We describe the corresponding class of models, which are Kripke models with a naturally arising notion of probability, and give a sound and complete infinitary axiomatic system. We prove that the logic is decidable.

1. Imagine that all our beliefs are organized as a web. Let us also imagine that there is a hierarchy among our beliefs. The stronger beliefs, located closer to the centre of the web, underpin the...

RésuméLa distinction d’Avicenne entre existence externe et existence mentale est fondamentale pour la logique et la philosophie de la tradition islamique. Cet article examine les philosophes qui s’écartent du cadre d’existence externe-mentale d’Avicenne. Ils considèrent que la première ne permet pas de soutenir une analyse générale de la réalité et de la vérité, car l’existence mentale n’est ni nécessaire ni suffisante pour analyser les vérités propositionnelles, c’est-à-dire que les propositions vraies sont vraies indépendamment de «l’existence même des esprits» et des (...) «actes perceptifs des percepteurs». Ils soutiennent que les conditions de vérité d’Avicenne doivent être révisées, car il existe de vraies propositions métathétiques et hypothétiques, c’est-à-dire que les termes sujets n’ont pas besoin d’exister – dans la réalité externe ou dans un esprit – pour que de telles propositions soient vraies. Ce courant de pensée contraire à celui d’Avicenne articule une troisième distinction dans l’analyse de la réalité. Ils se concentrent sur la nature indépendante de l’esprit du contenu propositionnel – en particulier les propositions avec des termes sujets vides, hypothétiques ou impossibles – comme moyen de penser la réalité de manière générale, contrairement à l’accent mis par Avicenne sur le statut existentiel des termes et des essences. Notamment, l’analyse de la réalité indépendante de l’esprit est soutenue par une nouvelle sémantique des propositions catégoriques «réelles» (ḥaqīqī), qui évite les conditions d’existence externes et mentales d’Avicenne. (shrink)

Sahlqvist formulas are a syntactically specified class of modal formulas proposed by Hendrik Sahlqvist in 1975. They are important because of their first-order definability and canonicity, and hence axiomatize complete modal logics. The first-order properties definable by Sahlqvist formulas were syntactically characterized by Marcus Kracht in 1993. The present paper extends Kracht's theorem to the class of ‘generalized Sahlqvist formulas' introduced by Goranko and Vakarelov and describes an appropriate generalization of Kracht formulas.

If two self-connected individuals are connected, it follows in classical extensional mereotopology that the sum of those individuals is self-connected too. Since mainland Europe and mainland Asia, for example, are both self-connected and connected to each other, mainland Eurasia is also self-connected. In contrast, in non-extensional mereotopologies, two individuals may have more than one sum, in which case it does not follow from their being self-connected and connected that the sum of those individuals is self-connected too. Nevertheless, one would still (...) expect it to follow that a sum of connected self-connected individuals is self-connected too. In this paper, we present some surprising countermodels which show that this conjecture is incorrect. (shrink)

We extend Gurevich-Harrington's Restricted Memory Determinacy Theorem), which served in their paper as a tool to give their celebrated “short proof” of Robin's decision method for S2S. We generalize the determinacy problem by attaching to the game two opposing strategies called restraints, and by asking “which player has a strategy which is a refinement of the restraint for the player and such that it wins the game against the restraint of the opponent?” We give a solution for the Determinacy with (...) Restraints Problem in the class of strategies with restricted memory for the GH games. The solution includes a criterion for the winning player and an explicit class of winning strategies. A determinacy result which includes similar information was first discovered by Büchi and Landweber and extended by Büchi . However, these pioneering works do not consider the determinacy with restraints. Also, the explicit presentation of winning strategies in these insightful papers does not emphasize their modular construction as do GH's and our proofs. In our view, this is a source of a difficulty in understanding these papers. Games with restraints and modular construction of winning strategies have applications to the semantics, development and verification of concurrent programs. A concurrent program can be viewed as a strategy in a certain game and a program specification can be regarded as a combination of a winning condition and restraints for the game , A. Yakhnis and V. Yakhnis ). The modularity of a winning strategyfor the game helps to generate a concurrent program from the strategy that satisfies the specification ). It turns out that such program specification requirements as mutual exclusion and an absence of a lockout or a deadlock are naturally represented as Büchi's or Gurevich-Harrington's winning conditions. The present paper can be read independently of the paper by Gurevich and Harrington. (shrink)

The purpose of this paper is to examine in detail a particularly interesting pair of first-order theories. In addition to clarifying the overall geography of notions of equivalence between theories, this simple example yields two surprising conclusions about the relationships that theories might bear to one another. In brief, we see that theories lack both the Cantor-Bernstein and co-Cantor-Bernstein properties.

Some bioethicists have questioned the desirability of a line of biomedical research aimed at extending the length of our lives over what some think to be its natural limit. In particular, Leon Kass has argued that living longer is not such a great advantage, and that mortality is not a burden after all. In this essay, I evaluate his arguments in favour of such a counterintuitive view by elaborating upon some critical remarks advanced by John Harris. Ultimately, I argue that (...) nothing substantial has been said by Kass to undermine the desirability of life-extending technologies. (shrink)

In this paper, we generalize the definition of Neutrosophic sets and present a method for extending crisp functions on Neutrosophic sets and study some properties of such extended functions.

Recent developments in biogerontology—the study of the biology of ageing—suggest that it may eventually be possible to intervene in the human ageing process. This, in turn, offers the prospect of significantly postponing the onset of age-related diseases. The biogerontological project, however, has met with strong resistance, especially by deontologists. They consider the act of intervening in the ageing process impermissible on the grounds that it would (most probably) bring about an extended maximum lifespan—a state of affairs that they deem intrinsically (...) bad. In a bid to convince their deontological opponents of the permissibility of this act, proponents of biogerontology invoke an argument which is grounded in the doctrine of double effect. Surprisingly, their argument, which we refer to as the ‘double effect argument’, has gone unnoticed. This article exposes and critically evaluates this ‘double effect argument’. To this end, we first review a series of excerpts from the ethical debate on biogerontology in order to substantiate the presence of double effect reasoning. Next, we attempt to determine the role that the ‘double effect argument’ is meant to fulfil within this debate. Finally, we assess whether the act of intervening in ageing actually can be justified using double effect reasoning. (shrink)

Bu çalışma İslam mantık literatüründeki kavramlar ve önermeler arasındaki kaplamsal bağıntıları konu edinir. Kavram bağıntıları klasik mantığın iki önemli konusu olan tanım ve kıyas alanlarında önemli bir yer tutar, çünkü bir tanım cümlesinin kavramları arasındaki genellik-özellik ilişkisi onun sahihliğini denetlemede, kıyasın kavramları arasındaki ilişkiler de onun tutarlılığını denetlemede işe yarar. Önerme bağıntıları ise bir kıyasın geçerli netice vermesindeki özel şartları belirleyen öncülün tespiti için önemlidir. Bu makalede giriş olarak bağıntıların ne olduğunu açıkladıktan sonra, kavramlar ve önermeler arasındaki bağıntıların İslam mantık (...) geleneğindeki tarihsel gelişimini ayrı başlıklar altında ele alıyoruz. İslam mantıkçıları kavramlar ya da önermeler arasında oluşabilecek dört bağıntıyı “en-nisebü’l-erba‘” terimiyle ifade ederler. Bu terimin altında toplanan dört bağıntı biçimi şunlardır: Tam kapsama-kapsanma bağıntısı (umûm ve husûs mutlak), kısmî kapsama-kapsanma bağıntısı (umûm ve husûs min vech), eşitlik (müsâvât) ve ayrıklık (mübâyenet) bağıntıları. İslam mantıkçıları benzer şekilde bağıntıların, önermeler arasında kipleri ve doğruluk kriterlerine göre de ortaya çıkabileceğini düşünerek bu meseleyi daha ayrıntılı biçimde ele almış ve genişletmiştir. (shrink)

Extensive measurement is the standard measurement-theoretic approach for constructing a ratio scale. It involves the comparison of objects that can be concatenated in an additively representable way. This paper studies the implications of extensively measurable welfare for social choice theory. We do this in two frameworks: an Arrovian framework with a fixed population and no interpersonal comparisons, and a generalized framework with variable populations and full interpersonal comparability. In each framework we use extensive measurement to introduce novel domain restrictions, independence (...) conditions, and constraints on social evaluation. We prove a welfarism theorem for these domains and characterize the social welfare functions that satisfy the axioms of extensive measurement at both the individual and social levels. The main results are simple axiomatizations of strong dictatorship in the Arrovian framework and classical utilitarianism in the generalized framework. (shrink)

Technological advances in computer science have secured the computer metaphor status of a heuristic methodological tool used to answer the question about the nature of mind. Nevertheless, some philosophers strongly support opposite opinions. Anti-computationalism in the philosophy of mind is a methodological program that uses extremely heterogeneous grounds for argumentation, deserving analysis and discussion. This article provides an overview and interpretation of the traditional criticism of the computational theory of mind ; its basic theses have been formed in Western philosophy (...) in the last quarter of the 20th century. The main goal is to reveal the content of the arguments of typical anti-computationalist programs and expand their application to the framework of the semantic problems of the Classic Computational Theory of Mind. The main fault of the symbolic ap-proach in the classical computationalism is the absence of a full-fledged theory of semantic properties. The relevance of considering these seemingly outdated problems is justified by the fact that the problem of meaning remains in the core of the latest developments in various areas of AI and the principles of human-computer interaction. (shrink)

This study focuses on the devices implemented in classical Indian texts on ritual and language in order to develop a structure of rules in an economic and systematic way. These devices presuppose a spatial approach to ritual and language, one which deals for instance with absences as substitutions within a pre-existing grid, and not as temporal disappearances. In this way, the study reveals a key feature of some among the most influential schools of Indian thought. The sources are Kalpasūtra, Vyākaraṇa (...) and Mīmāṃsā, three textual traditions which developed alongside each other, sharing - as the volume shows - common presuppositions and methodologies. The book will be of interest for Sanskritists, scholars of ritual exegesis and of the history of linguistics. - Cover. (shrink)

The novelty-seeking model suggests that curiosity and creativity originate from novelty processes. However, different types of novelty exist, each with distinctive relationships with memory, which potentially influence curiosity and creativity in distinct ways. We thus propose expanding the NSM model to consider these different novelty types and their specific involvement in creativity.

May's Theorem [K. O. May, Econometrica 20 (1952) 680-684] characterizes majority voting on two alternatives as the unique preferential voting method satisfying several simple axioms. Here we show that by adding some desirable axioms to May's axioms, we can uniquely determine how to vote on three alternatives. In particular, we add two axioms stating that the voting method should mitigate spoiler effects and avoid the so-called strong no show paradox. We prove a theorem stating that any preferential voting method satisfying (...) our enlarged set of axioms, which includes some weak homogeneity and preservation axioms, agrees with Minimax voting in all three-alternative elections, except perhaps in some improbable knife-edged elections in which ties may arise and be broken in different ways. (shrink)

Educational assessments tests are often constructed using testlets because of the flexibility to test various aspects of the cognitive activities and broad content sampling. However, the violation of the local item independence assumption is inevitable when tests are built using testlet items. In this study, simulations are conducted to evaluate the performance of item response theory models and testlet response theory models for both the dichotomous and polytomous items in the context of equating tests composed of testlets. We also examine (...) the impact of testlet effect, length of testlet items, and sample size on estimating item and person parameters. The results show that more accurate performance of testlet response theory models over item response theory models was consistently observed across the studies, which supports the benefits of using the testlet response theory models in equating for tests composed of testlets. Further, results of the study indicate that when sample size is large, item response theory models performed similarly to testlet response theory models across all studies. (shrink)

This article extends the combinatorial approach to support the determination of contextuality amidst causal influences. Contextuality is an active field of study in Quantum Cognition, in systems relating to mental phenomena, such as concepts in human memory. In the cognitive field of study, a contemporary challenge facing the determination of whether a phenomenon is contextual has been the identification and management of disturbances. Whether or not said disturbances are identified through the modeling approach, constitute causal influences, or are disregardableas as (...) noise is important, as contextuality cannot be adequately determined in the presence of causal influences. To address this challenge, we first provide a formalization of necessary elements of the combinatorial approach within the language of canonical causal models. Through this formalization, we extend the combinatorial approach to support a measurement and treatment of disturbance, and offer techniques to separately distinguish noise and causal influences. Thereafter, we develop a protocol through which these elements may be represented within a cognitive experiment. As human cognition seems rife with causal influences, cognitive modelers may apply the extended combinatorial approach to practically determine the contextuality of cognitive phenomena. (shrink)