Статті в журналах: "Intensional logic"

1

Anderson, C. Anthony. "Zalta's intensional logic." Philosophical Studies 69, no. 2-3 (March 1993): 221–29. http://dx.doi.org/10.1007/bf00990086.

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2

Majkić, Zoran. "Conservative Intensional Extension of Tarski's Semantics." Advances in Artificial Intelligence 2013 (February 26, 2013): 1–10. http://dx.doi.org/10.1155/2013/920157.

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We considered an extension of the first-order logic (FOL) by Bealer's intensional abstraction operator. Contemporary use of the term “intension” derives from the traditional logical Frege-Russell doctrine that an idea (logic formula) has both an extension and an intension. Although there is divergence in formulation, it is accepted that the “extension” of an idea consists of the subjects to which the idea applies, and the “intension” consists of the attributes implied by the idea. From the Montague's point of view, the meaning of an idea can be considered as particular extensions in different possible worlds. In the case of standard FOL, we obtain a commutative homomorphic diagram, which is valid in each given possible world of an intensional FOL: from a free algebra of the FOL syntax, into its intensional algebra of concepts, and, successively, into an extensional relational algebra (different from Cylindric algebras). Then we show that this composition corresponds to the Tarski's interpretation of the standard extensional FOL in this possible world.

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3

Priest, Graham. "Intensional paradoxes." Notre Dame Journal of Formal Logic 32, no. 2 (March 1991): 193–211. http://dx.doi.org/10.1305/ndjfl/1093635745.

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4

Leone, Nicola, Luigi Palopoli, and Massimo Romeo. "MODIFYING INTENSIONAL LOGIC KNOWLEDGE." Fundamenta Informaticae 21, no. 3 (1994): 183–203. http://dx.doi.org/10.3233/fi-1994-2132.

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5

da Costa, Newton C. A., and Décio Krause. "An Intensional Schrödinger Logic." Notre Dame Journal of Formal Logic 38, no. 2 (April 1997): 179–94. http://dx.doi.org/10.1305/ndjfl/1039724886.

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6

Fitting, Melvin. "First-order intensional logic." Annals of Pure and Applied Logic 127, no. 1-3 (June 2004): 171–93. http://dx.doi.org/10.1016/j.apal.2003.11.014.

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7

Jiang, Yue J. "An intensional epistemic logic." Studia Logica 52, no. 2 (1993): 259–80. http://dx.doi.org/10.1007/bf01058391.

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8

Bull, R. A., and Johan van Benthem. "A Manual of Intensional Logic." Journal of Symbolic Logic 54, no. 4 (December 1989): 1489. http://dx.doi.org/10.2307/2274837.

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9

Payne, Jonathan. "Extensionalizing Intensional Second-Order Logic." Notre Dame Journal of Formal Logic 56, no. 1 (2015): 243–61. http://dx.doi.org/10.1215/00294527-2835092.

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10

Cocchiarella, Nino B. "Conceptualism, realism, and intensional logic." Topoi 8, no. 1 (March 1989): 15–34. http://dx.doi.org/10.1007/bf00138676.

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11

Ramsay, Allan. "Theorem proving for intensional logic." Journal of Automated Reasoning 14, no. 2 (1995): 237–55. http://dx.doi.org/10.1007/bf00881857.

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12

RONDOGIANNIS, P., and W. W. WADGE. "Higher-order functional languages and intensional logic." Journal of Functional Programming 9, no. 5 (September 1999): 527–64. http://dx.doi.org/10.1017/s0956796899003445.

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In this paper we demonstrate that a broad class of higher-order functional programs can be transformed into semantically equivalent multidimensional intensional programs that contain only nullary variable definitions. The proposed algorithm systematically eliminates user-defined functions from the source program, by appropriately introducing context manipulation (i.e. intensional) operators. The transformation takes place in M steps, where M is the order of the initial functional program. During each step the order of the program is reduced by one, and the final outcome of the algorithm is an M-dimensional intensional program of order zero. As the resulting intensional code can be executed in a purely tagged-dataflow way, the proposed approach offers a promising new technique for the implementation of higher-order functional languages.

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13

Маркин, В. И. "What trends in non-classical logic were anticipated by Nikolai Vasiliev?" Logical Investigations 19 (April 9, 2013): 122–35. http://dx.doi.org/10.21146/2074-1472-2013-19-0-122-135.

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In this paper we discuss a question about the trends in non-classical logic that were exactly anticipated by Niko- lai Vasiliev. We show the influence of Vasiliev’s Imaginary logic on paraconsistent logic. Metatheoretical relations between Vasiliev’s logical systems and many-valued predicate logics are established. We also make clear that Vasiliev has developed a sketch of original system of intensional logic and expressed certain ideas of modal and temporal logics.

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14

Surendonk, Timothy J. "Canonicity for Intensional Logics with Even Axioms." Journal of Symbolic Logic 66, no. 3 (September 2001): 1141–56. http://dx.doi.org/10.2307/2695098.

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AbstractThis paper looks at the concept of neighborhood canonicity introduced by Brian Chellas [2]. We follow the lead of the author's paper [9] where it was shown that every non-iterative logic is neighborhood canonical and here we will show that all logics whose axioms have a simple syntactic form—no intensional operator is in boolean combination with a propositional letter—and which have the finite model property are neighborhood canonical. One consequence of this is that KMcK, the McKinsey logic, is neighborhood canonical, an interesting counterpoint to the results of Robert Goldblatt and Xiaoping Wang who showed, respectively, that KMcK is not relational canonical [5] and that KMcK is not relationally strongly complete [11].

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15

Anderson, C. Anthony. "Some Difficulties Concerning Russellian Intensional Logic." Noûs 20, no. 1 (March 1986): 35. http://dx.doi.org/10.2307/2215278.

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16

Brauner, T. "Adding Intensional Machinery to Hybrid Logic." Journal of Logic and Computation 18, no. 4 (November 22, 2007): 631–48. http://dx.doi.org/10.1093/logcom/exn005.

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17

van Lee, Hanna S., Rasmus K. Rendsvig, and Suzanne van Wijk. "Intensional Protocols for Dynamic Epistemic Logic." Journal of Philosophical Logic 48, no. 6 (May 28, 2019): 1077–118. http://dx.doi.org/10.1007/s10992-019-09508-w.

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18

Belnap, Nuel, and Thomas Müller. "CIFOL: Case-Intensional First Order Logic." Journal of Philosophical Logic 43, no. 2-3 (January 20, 2013): 393–437. http://dx.doi.org/10.1007/s10992-012-9267-x.

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19

Muskens, Reinhard. "Intensional models for the theory of types." Journal of Symbolic Logic 72, no. 1 (March 2007): 98–118. http://dx.doi.org/10.2178/jsl/1174668386.

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AbstractIn this paper we define intensional models for the classical theory of types, thus arriving at an intensional type logic ITL. Intensional models generalize Henkin's general models and have a natural definition. As a class they do not validate the axiom of Extensionality. We give a cut-free sequent calculus for type theory and show completeness of this calculus with respect to the class of intensional models via a model existence theorem. After this we turn our attention to applications. Firstly, it is argued that, since ITL is truly intensional, it can be used to model ascriptions of propositional attitude without predicting logical omniscience. In order to illustrate this a small fragment of English is defined and provided with an ITL semantics. Secondly, it is shown that ITL models contain certain objects that can be identified with possible worlds. Essential elements of modal logic become available within classical type theory once the axiom of Extensionality is given up.

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20

Johnston, S. C. "Robert Kilwardby’s Science of Logic: A Thirteenth-Century Intensional Logic." History and Philosophy of Logic 41, no. 3 (May 19, 2020): 301–3. http://dx.doi.org/10.1080/01445340.2020.1757889.

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21

Lapierre, Serge. "A functional partial semantics for intensional logic." Notre Dame Journal of Formal Logic 33, no. 4 (September 1992): 517–41. http://dx.doi.org/10.1305/ndjfl/1093634484.

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22

Swoyer, Chris, and Edward Zalta. "Intensional Logic and the Metaphysics of Intentionality." Noûs 27, no. 2 (June 1993): 243. http://dx.doi.org/10.2307/2215760.

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23

Zimmermann, Thomas Ede. "Intensional logic and two-sorted type theory." Journal of Symbolic Logic 54, no. 1 (March 1989): 65–77. http://dx.doi.org/10.2307/2275016.

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Among the symbolic languages used most frequently in the indirect interpretation of natural language are Montague's Intensional Logic IL [5, 384ff.] and its extensional counterpart, the language Ty2 of two-sorted type theory. The question of which of these two formal languages is to be preferred has been obscured by lack of knowledge about the exact relation between them. The present paper is an attempt to clarify the situation by showing that, modulo a small, decidable class of formulas irrelevant to these applications, IL and Ty2 are equivalent in the strong sense that there exists a reversible translation between the terms of either language.In [3, 6Iff.] Gallin has shown that there exists a simple and natural translation * of IL into Ty2. Following Gallin's translation procedure, it is even possible to conceive of IL as a highly restricted sublanguage of Ty2, viz. as that part which only contains expressions of certain intensional types plus one variable of the basic type of indices or worlds. In an obvious sense, this sublanguage has less expressive power than the whole of Ty2, where it is possible to express conditions on entities that do not even exist in IL's ontology. However, by a certain amount of coding, one can translate Ty2 into IL [3, 105]. Conditions on nonintensional entities then become conditions on corresponding intensional objects; and these paraphrases preserve (standard) validity and entailment. On the other hand, this retranslation of Ty2 into IL is not an inversion of *, as can be seen from a simple example.

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24

Jacquette, Dale, and Edward N. Zalta. "Intensional Logic and the Metaphysics of Intentionality." Philosophy and Phenomenological Research 51, no. 2 (June 1991): 439. http://dx.doi.org/10.2307/2108142.

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25

Hazen, A. P., and Edward N. Zalta. "Intensional Logic and the Metaphysics of Intentionality." Philosophical Review 100, no. 3 (July 1991): 474. http://dx.doi.org/10.2307/2185073.

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26

RONDOGIANNIS, P., and W. W. WADGE. "First-order functional languages and intensional logic." Journal of Functional Programming 7, no. 1 (January 1997): 73–101. http://dx.doi.org/10.1017/s0956796897002633.

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The purpose of this paper is to demonstrate that first-order functional programs can be transformed into intensional programs of nullary variables, in a semantics preserving way. On the foundational side, the goal of our study is to bring new insights and a better understanding of the nature of functional languages. From a practical point of view, our investigation provides a formal basis for the tagging mechanism that is used in the implementation of first-order functional languages on dataflow machines.

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27

GLASHOFF, KLAUS. "AN INTENSIONAL LEIBNIZ SEMANTICS FOR ARISTOTELIAN LOGIC." Review of Symbolic Logic 3, no. 2 (March 17, 2010): 262–72. http://dx.doi.org/10.1017/s1755020309990396.

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Since Frege’s predicate logical transcription of Aristotelian categorical logic, the standard semantics of Aristotelian logic considers terms as standing for sets of individuals. From a philosophical standpoint, this extensional model poses problems: There exist serious doubts that Aristotle’s terms were meant to refer always to sets, that is, entities composed of individuals. Classical philosophy up to Leibniz and Kant had a different view on this question—they looked at terms as standing for concepts (“Begriffe”). In 1972, Corcoran presented a formal system for Aristotelian logic containing a calculus of natural deduction, while, with respect to semantics, he still made use of an extensional interpretation. In this paper we deal with a simple intensional semantics for Corcoran’s syntax—intensional in the sense that no individuals are needed for the construction of a complete Tarski model of Aristotelian syntax. Instead, we view concepts as containing or excluding other, “higher” concepts—corresponding to the idea which Leibniz used in the construction of his characteristic numbers. Thus, this paper is an addendum to Corcoran’s work, furnishing his formal syntax with an adequate semantics which is free from presuppositions which have entered into modern interpretations of Aristotle’s theory via predicate logic.

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28

Du, W., and W. W. Wadge. "A 3D spreadsheet based on intensional logic." IEEE Software 7, no. 3 (May 1990): 78–89. http://dx.doi.org/10.1109/52.55232.

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29

Belnap, Nuel, and Thomas Müller. "BH-CIFOL: Case-Intensional First Order Logic." Journal of Philosophical Logic 43, no. 5 (August 25, 2013): 835–66. http://dx.doi.org/10.1007/s10992-013-9292-4.

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30

Duží, Marie, and Aleš Horák. "Hyperintensional Reasoning Based on Natural Language Knowledge Base." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 28, no. 03 (May 21, 2020): 443–68. http://dx.doi.org/10.1142/s021848852050018x.

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The success of automated reasoning techniques over large natural-language texts heavily relies on a fine-grained analysis of natural language assumptions. While there is a common agreement that the analysis should be hyperintensional, most of the automatic reasoning systems are still based on an intensional logic, at the best. In this paper, we introduce the system of reasoning based on a fine-grained, hyperintensional analysis. To this end we apply Tichy’s Transparent Intensional Logic (TIL) with its procedural semantics. TIL is a higher-order, hyperintensional logic of partial functions, in particular apt for a fine-grained natural-language analysis. Within TIL we recognise three kinds of context, namely extensional, intensional and hyperintensional, in which a particular natural-language term, or rather its meaning, can occur. Having defined the three kinds of context and implemented an algorithm of context recognition, we are in a position to develop and implement an extensional logic of hyperintensions with the inference machine that should neither over-infer nor under-infer.

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31

Moschovakis, Yiannis N. "The formal language of recursion." Journal of Symbolic Logic 54, no. 4 (December 1989): 1216–52. http://dx.doi.org/10.1017/s0022481200041086.

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This is the first of a sequence of papers in which we will develop a foundation for the theory of computation based on a precise, mathematical notion of abstract algorithm. To understand the aim of this program, one should keep in mind clearly the distinction between an algorithm and the object (typically a function) computed by that algorithm. The theory of computable functions (on the integers and on abstract structures) is obviously relevant to this work, but we will focus on making rigorous and identifying the mathematical properties of the finer (intensional) notion of algorithm.It is characteristic of this approach that we take recursion to be a fundamental (primitive) process for constructing algorithms, not a derived notion which must be reduced to others—e.g. iteration or application and abstraction, as in the classical λ-calculus. We will model algorithms by recursors, the set-theoretic objects one would naturally choose to represent (syntactically described) recursive definitions. Explicit and iterative algorithms are modelled by (appropriately degenerate) recursors.The main technical tool we will use is the formal language of recursion, FLR, a language of terms with two kinds of semantics: on each suitable structure, the denotation of a term t of FLR is a function, while the intension of t is a recursor (i.e. an algorithm) which computes the denotation of t. FLR is meant to be intensionally complete, in the sense that every (intuitively understood) “algorithm” should “be” (faithfully modelled, in all its essential properties by) the intension of some term of FLR on a suitably chosen structure.

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32

Magryś, Roman. "Prawda i fałsz wypowiedzi literackiej." Dydaktyka Polonistyczna 15, no. 6 (2020): 72–91. http://dx.doi.org/10.15584/dyd.pol.15.2020.5.

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The article “Truth and Falsity of Literary Statements” investigates the issue of logical values, and consequently communication related status of sentences in indicative mood occurring in works of literature. The problem is discussed with reference to theoretical assumptions of classical logic, intuitionistic logic, and other possible intensional logics as well as phenomenological concepts proposed by Roman Ingarden. In this context it is suggested that intensional systems, mainly intuitionistic logic be adequately applied to identify logical value of literary sentences. As a result, it is assumed that the logical value of literary sentences depends on the specific logical system selected; according to the standards of intuitionistic logic, literary statements are true, likely or false. In this context it seems necessary to revise Roman Ingarden’s phenomenological assumption that sentences in indicative mood in a work of fiction do not have objective point of reference. It is suggested that such sentences be recognised as false, and therefore indicative of the group of their intentional meanings as a specific model of reality which can be deemed true or false.

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33

Hanson, William H., and James Hawthorne. "Validity in intensional languages: a new approach." Notre Dame Journal of Formal Logic 26, no. 1 (January 1985): 9–35. http://dx.doi.org/10.1305/ndjfl/1093870758.

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34

Carlström, Jesper. "Interpreting descriptions in intensional type theory." Journal of Symbolic Logic 70, no. 2 (June 2005): 488–514. http://dx.doi.org/10.2178/jsl/1120224725.

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AbstractNatural deduction systems with indefinite and definite descriptions (ε-terms and ι-terms) are presented, and interpreted in Martin-LÖf's intensional type theory. The interpretations are formalizations of ideas which are implicit in the literature of constructive mathematics: if we have proved that an element with a certain property exists, we speak of ‘the element such that the property holds’ and refer by that phrase to the element constructed in the existence proof. In particular, we deviate from the practice of interpreting descriptions by contextual definitions.

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35

Redding, Paul. "Hegel’s Subjective Logic as a Logic for (Hegel’s) Philosophy of Mind." Hegel Bulletin 39, no. 1 (October 17, 2016): 1–22. http://dx.doi.org/10.1017/hgl.2016.54.

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AbstractIn the 1930s, C. I. Lewis, who was responsible for the revival of modal logic in the era of modern symbolic logic, characterized ‘intensional’ approaches to logic as typical of post-Leibnizian ‘continental philosophy’, in contrast to the ‘extensionalist’ approaches dominant in the British tradition. Indeed Lewis’s own work in this area had been inspired by the logic of his teacher, the American ‘Absolute Idealist’, Josiah Royce. Hegel’s ‘Subjective Logic’ in Book III of hisScience of Logic, can, I suggest, be considered as an intensional modal logic, and this paper explores parallels between it and a later variety of modal logic—tenselogic, as developed by Arthur Prior in the 1950s and 60s. Like Lewis, Prior too had been influenced in this area by a teacher with strong Hegelian leanings—John N. Findlay. Treated as anintensional(with an ‘s’) logic, Hegel’s subjective logic can be used as a framework for addressing issues ofintentionality(with a ‘t’)—the mind’s capacity to be intentionally directed to objects. In this way, I suggest that the structures of his subjective logic can clarify what is at issue in the ‘Psychology’ section of theEncyclopaediaPhilosophy of Subjective Spirit.

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36

Anderson, C. Anthony. "Alonzo Church's Contributions to Philosophy and Intensional Logic." Bulletin of Symbolic Logic 4, no. 2 (June 1998): 129–71. http://dx.doi.org/10.2307/421020.

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§0. Alonzo Church's contributions to philosophy and to that most philosophical part of logic, intensional logic, are impressive indeed. He wrote relatively few papers actually devoted to specifically philosophical issues, as distinguished from related technical work in logic. Many of his contributions appear in reviews for The Journal of Symbolic Logic, and it can hardly be maintained that one finds there a “philosophical system”. But there occur a clearly articulated and powerful methodology, terse arguments, often of “crushing cogency”, and philosophical observations of the first importance.Many of the less formal philosophical contributions center around questions concerning meaning, but there are important clarifications and insights into matters of the epistemology and ontology of the sciences, especially the formal sciences.1.1. The logistic method. Church's writings on philosophical matters exhibit an unwavering commitment to what he called the “logistic method”. The term did not catch on and now one would just speak of “formalization”. The use of these ideas is now so common and familiar among logicians and logically-oriented philosophers that they are simply taken for granted. But they deserve to be celebrated and re-emphasized, for there are (still) philosophers who seriously underestimate and even consciously reject these techniques.

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37

Morra, Lucia. "Traduzione e filosofia analitica: prima di Quine." PARADIGMI, no. 2 (July 2009): 17–31. http://dx.doi.org/10.3280/para2009-002003.

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- This paper is a survey of the analytical theories of translation prior to Quine's writings on this subject, which must be read in the light of previous discussion and the observations of authors such as Frege, Russell, Wittgenstein, Schlick and Carnap. Translation became an issue of major importance in analytical philosophy in the second half of the last century. Born as a query concerning a very specific task (translating mathematics into logic), the problem of translation became increasingly more general: in the Thirties, the point was to find a general method for translating all sorts of formal languages; only in the Fifties and later on, it focused on the general conditions of translating.Keywords: Logical translation, Reversible translation, Translation scalarity, Intensional isomorphism, Carnap, Wittgenstein. Alberto Voltolini, L'irrimediabile dilemma del traduttoreParole chiave: Traduzione logica, Traduzione reversibile, Scalaritŕ della traduzione, Isomorfismo intensionale, Carnap, Wittgenstein.

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38

GAO, YING, and JINGDE CHENG. "Semantics for a basic relevant logic with intensional conjunction and disjunction (and some of its extensions)." Mathematical Structures in Computer Science 18, no. 1 (February 2008): 145–64. http://dx.doi.org/10.1017/s0960129508006592.

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This paper proposes a new relevant logic B+⊓⊔, which is obtained by adding two binary connectives, intensional conjunction ⊓ and intensional disjunction ⊔, to Meyer–Routley minimal positive relevant logic B+, where ⊓ and ⊔ are weaker than fusion ˚ and fission +, respectively. We give Kripke-style semantics for B+⊓⊔, with →, ⊓ and ⊔ modelled by ternary relations. We prove the soundness and completeness of the proposed semantics. A number of axiomatic extensions of B+⊓⊔, including negation-extensions, are also considered, together with the corresponding semantic conditions required for soundness and completeness to be maintained.

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39

Bacon, Andrew, John Hawthorne, and Gabriel Uzquiano. "Higher-order free logic and the Prior-Kaplan paradox." Canadian Journal of Philosophy 46, no. 4-5 (August 2016): 493–541. http://dx.doi.org/10.1080/00455091.2016.1201387.

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AbstractThe principle of universal instantiation plays a pivotal role both in the derivation of intensional paradoxes such as Prior's paradox and Kaplan's paradox and the debate between necessitism and contingentism. We outline a distinctively free logical approach to the intensional paradoxes and note how the free logical outlook allows one to distinguish two different, though allied themes in higher-order necessitism. We examine the costs of this solution and compare it with the more familiar ramificationist approaches to higher-order logic. Our assessment of both approaches is largely pessimistic, and we remain reluctantly inclined to take Prior's and Kaplan's derivations at face value.

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40

Galanaki, Chrysida, Christos Nomikos, and Panos Rondogiannis. "Game semantics for non-monotonic intensional logic programming." Annals of Pure and Applied Logic 168, no. 2 (February 2017): 234–53. http://dx.doi.org/10.1016/j.apal.2016.10.005.

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41

Alves, E. H., and J. A. D. Guerzoni. "Extending Montague's system: a three valued intensional logic." Studia Logica 49, no. 1 (March 1990): 127–32. http://dx.doi.org/10.1007/bf00401558.

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42

Orgun, Mehmet A., and William W. Wadge. "Towards a unified theory of intensional logic programming." Journal of Logic Programming 13, no. 4 (August 1992): 413–40. http://dx.doi.org/10.1016/0743-1066(92)90055-8.

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43

Balbiani, Philippe. "A Modal Semantics of Negation in Logic Programming." Fundamenta Informaticae 16, no. 3-4 (May 1, 1992): 231–62. http://dx.doi.org/10.3233/fi-1992-163-403.

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The beauty of modal logics and their interest lie in their ability to represent such different intensional concepts as knowledge, time, obligation, provability in arithmetic, … according to the properties satisfied by the accessibility relations of their Kripke models (transitivity, reflexivity, symmetry, well-foundedness, …). The purpose of this paper is to study the ability of modal logics to represent the concepts of provability and unprovability in logic programming. The use of modal logic to study the semantics of logic programming with negation is defended with the help of a modal completion formula. This formula is a modal translation of Clack’s formula. It gives soundness and completeness proofs for the negation as failure rule. It offers a formal characterization of unprovability in logic programs. It characterizes as well its stratified semantics.

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44

Gaines, Brian R., and Mildred L. G. Shaw. "Knowledge acquisition tools based on personal construct psychology." Knowledge Engineering Review 8, no. 1 (March 1993): 49–85. http://dx.doi.org/10.1017/s0269888900000060.

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AbstractKnowledge acquisition research supports the generation of knowledge-based systems through the development of principles, techniques, methodologies and tools. What differentiates knowledge-based system development from conventional system development is the emphasis on in-depth understanding and formalization of the relations between the conceptual structures underlying expert performance and the computational structures capable of emulating that performance.Personal construct psychology is a theory of individual and group psychological and social processes that has been used extensively in knowledge acquisition research to model the cognitive processes of human experts. The psychology takes a constructivist position appropriate to the modelling of human knowledge processes, but develops this through the characterization of human conceptual structures in axiomatic terms that translate directly to computational form. In particular, there is a close correspondence between the intensional logics of knowledge, belief and action developed in personal construct psychology, and the intensional logics for formal knowledge representation developed in artificial intelligence research as term subsumption, or KL-ONE-like, systems.This paper gives an overview of personal construct psychology and its expression as an intensional logic describing the cognitive processes of anticipatory agents, and uses this to survey knowledge acquisition tools deriving from personal construct psychology.

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45

Preller, A., and N. Lafaye De Micheaux. "Intensional Equality in Categories With Structure and Coherence Problems." Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 34, no. 5 (1988): 421–32. http://dx.doi.org/10.1002/malq.19880340506.

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46

Jäger, Gerhard. "An intensional fixed point theory over first order arithmetic." Annals of Pure and Applied Logic 128, no. 1-3 (August 2004): 197–213. http://dx.doi.org/10.1016/j.apal.2003.11.032.

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47

BARTHOLOMEW, MICHAEL, and JOOHYUNG LEE. "On the stable model semantics for intensional functions." Theory and Practice of Logic Programming 13, no. 4-5 (July 2013): 863–76. http://dx.doi.org/10.1017/s1471068413000549.

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AbstractSeveral extensions of the stable model semantics are available to describe ‘intensional’ functions—functions that can be described in terms of other functions and predicates by logic programs. Such functions are useful for expressing inertia and default behaviors of systems, and can be exploited for alleviating the grounding bottleneck involving functional fluents. However, the extensions were defined in different ways under different intuitions. In this paper we provide several reformulations of the extensions, and note that they are in fact closely related to each other and coincide on large syntactic classes of logic programs.

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48

Gilmore, Paul C. "An intensional type theory: motivation and cut-elimination." Journal of Symbolic Logic 66, no. 1 (March 2001): 383–400. http://dx.doi.org/10.2307/2694928.

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AbstractBy the theory TT is meant the higher order predicate logic with the following recursively defined types:(1) 1 is the type of individuals and [] is the type of the truth values:(2) [τ1…..τn] is the type of the predicates with arguments of the types τ1…..τn.The theory ITT described in this paper is an intensional version of TT. The types of ITT are the same as the types of TT, but the membership of the type 1 of individuals in ITT is an extension of the membership in TT. The extension consists of allowing any higher order term, in which only variables of type 1 have a free occurrence, to be a term of type 1. This feature of ITT is motivated by a nominalist interpretation of higher order predication.In ITT both well-founded and non-well-founded recursive predicates can be defined as abstraction terms from which all the properties of the predicates can be derived without the use of non-logical axioms.The elementary syntax, semantics, and proof theory for ITT are defined. A semantic consistency proof for ITT is provided and the completeness proof of Takahashi and Prawitz for a version of TT without cut is adapted for ITT: a consequence is the redundancy of cut.

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Pasquerella, Lynn. "INTENSIONAL LOGIC AND BRENTANO’S NON-PROPOSITIONAL THEORY OF JUDGMENT." Grazer Philosophische studien 29, no. 1 (August 13, 1987): 59–62. http://dx.doi.org/10.1163/18756735-90000309.

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Pezlar, Ivo. "On Two Notions of Computation in Transparent Intensional Logic." Axiomathes 29, no. 2 (September 14, 2018): 189–205. http://dx.doi.org/10.1007/s10516-018-9401-7.

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