Results for 'Linear Logic'

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  1. Modelling Combinatorial Auctions in Linear Logic.Daniele Porello & Ulle Endriss - 2010 - In Daniele Porello & Ulle Endriss (eds.), Principles of Knowledge Representation and Reasoning: Proceedings of the Twelfth International Conference, {KR} 2010, Toronto, Ontario, Canada, May 9-13, 2010.
    We show that linear logic can serve as an expressive framework in which to model a rich variety of combinatorial auction mechanisms. Due to its resource-sensitive nature, linear logic can easily represent bids in combinatorial auctions in which goods may be sold in multiple units, and we show how it naturally generalises several bidding languages familiar from the literature. Moreover, the winner determination problem, i.e., the problem of computing an allocation of goods to bidders producing a (...)
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  2. Modelling Multilateral Negotiation in Linear Logic.Daniele Porello & Ulle Endriss - 2010 - In Daniele Porello & Ulle Endriss (eds.), {ECAI} 2010 - 19th European Conference on Artificial Intelligence, Lisbon, Portugal, August 16-20, 2010, Proceedings. pp. 381--386.
    We show how to embed a framework for multilateral negotiation, in which a group of agents implement a sequence of deals concerning the exchange of a number of resources, into linear logic. In this model, multisets of goods, allocations of resources, preferences of agents, and deals are all modelled as formulas of linear logic. Whether or not a proposed deal is rational, given the preferences of the agents concerned, reduces to a question of provability, as does (...)
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  3. The ILLTP Library for Intuitionistic Linear Logic.Carlos Olarte, Valeria Correa Vaz De Paiva, Elaine Pimentel & Giselle Reis - manuscript
    Benchmarking automated theorem proving (ATP) systems using standardized problem sets is a well-established method for measuring their performance. However, the availability of such libraries for non-classical logics is very limited. In this work we propose a library for benchmarking Girard's (propositional) intuitionistic linear logic. For a quick bootstrapping of the collection of problems, and for discussing the selection of relevant problems and understanding their meaning as linear logic theorems, we use translations of the collection of Kleene's (...)
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  4. Non-normal modalities in variants of linear logic.D. Porello & N. Troquard - 2015 - Journal of Applied Non-Classical Logics 25 (3):229-255.
    This article presents modal versions of resource-conscious logics. We concentrate on extensions of variants of linear logic with one minimal non-normal modality. In earlier work, where we investigated agency in multi-agent systems, we have shown that the results scale up to logics with multiple non-minimal modalities. Here, we start with the language of propositional intuitionistic linear logic without the additive disjunction, to which we add a modality. We provide an interpretation of this language on a class (...)
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  5. From Linear to Branching-Time Temporal Logics: Transfer of Semantics and Definability.Valentin Goranko & Alberto Zanardo - 2007 - Logic Journal of the IGPL 15 (1):53-76.
    This paper investigates logical aspects of combining linear orders as semantics for modal and temporal logics, with modalities for possible paths, resulting in a variety of branching time logics over classes of trees. Here we adopt a unified approach to the Priorean, Peircean and Ockhamist semantics for branching time logics, by considering them all as fragments of the latter, obtained as combinations, in various degrees, of languages and semantics for linear time with a modality for possible paths. We (...)
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  6. Logics Based on Linear Orders of Contaminating Values.Roberto Ciuni, Thomas Macaulay Ferguson & Damian Szmuc - 2019 - Journal of Logic and Computation 29 (5):631–663.
    A wide family of many-valued logics—for instance, those based on the weak Kleene algebra—includes a non-classical truth-value that is ‘contaminating’ in the sense that whenever the value is assigned to a formula φ⁠, any complex formula in which φ appears is assigned that value as well. In such systems, the contaminating value enjoys a wide range of interpretations, suggesting scenarios in which more than one of these interpretations are called for. This calls for an evaluation of systems with multiple contaminating (...)
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  7. A resource-sensitive logic of agency.Daniele Porello & Nicolas Troquard - 2014 - In Ios Press (ed.), Proceedings of the 21st European Conference on Artificial Intelligence (ECAI'14), Prague, Czech Republic. 2014. pp. 723-728.
    We study a fragment of Intuitionistic Linear Logic combined with non-normal modal operators. Focusing on the minimal modal logic, we provide a Gentzen-style sequent calculus as well as a semantics in terms of Kripke resource models. We show that the proof theory is sound and complete with respect to the class of minimal Kripke resource models. We also show that the sequent calculus allows cut elimination. We put the logical framework to use by instantiating it as a (...)
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  8. Logical operators for ontological modeling.Stefano Borgo, Daniele Porello & Nicolas Troquard - 2014 - In Pawel Garbacz & Oliver Kutz (eds.), Formal Ontology in Information Systems - Proceedings of the Eighth International Conference, {FOIS} 2014, September, 22-25, 2014, Rio de Janeiro, Brazil}. pp. 23--36.
    We show that logic has more to offer to ontologists than standard first order and modal operators. We first describe some operators of linear logic which we believe are particularly suitable for ontological modeling, and suggest how to interpret them within an ontological framework. After showing how they can coexist with those of classical logic, we analyze three notions of artifact from the literature to conclude that these linear operators allow for reducing the ontological commitment (...)
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  9.  72
    Neutrosophic linear models and algorithms to find their optimal solution.Florentin Smarandache & Maissam Ahmad Jdid - 2023
    We present a study of linear models using the concepts of neutrosophic science, the science that was built on the basis that there is no absolute truth, there is no confirmed data, issues cannot be limited to right and wrong only. There is a third state between error and right, an indeterminate, undetermined, uncertain state. It is indeterminacy. Neutrosophic science gave each issue three dimensions, namely (T, I, F), correctness in degrees, indeterminacy in degrees, and error in degrees. It (...)
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  10. Tableaux-based decision method for single-agent linear time synchronous temporal epistemic logics with interacting time and knowledge.Mai Ajspur & Valentin Goranko - 2013 - In Kamal Lodaya (ed.), Logic and Its Applications. Springer. pp. 80--96.
    Temporal epistemic logics are known, from results of Halpern and Vardi, to have a wide range of complexities of the satisfiability problem: from PSPACE, through non-elementary, to highly undecidable. These complexities depend on the choice of some key parameters specifying, inter alia, possible interactions between time and knowledge, such as synchrony and agents' abilities for learning and recall. In this work we develop practically implementable tableau-based decision procedures for deciding satisfiability in single-agent synchronous temporal-epistemic logics with interactions between time and (...)
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  11. Logics for modelling collective attitudes.Daniele Porello - 2018 - Fundamenta Informaticae 158 (1-3):239-27.
    We introduce a number of logics to reason about collective propositional attitudes that are defined by means of the majority rule. It is well known that majoritarian aggregation is subject to irrationality, as the results in social choice theory and judgment aggregation show. The proposed logics for modelling collective attitudes are based on a substructural propositional logic that allows for circumventing inconsistent outcomes. Individual and collective propositional attitudes, such as beliefs, desires, obligations, are then modelled by means of minimal (...)
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  12. Collection Frames for Distributive Substructural Logics.Greg Restall & Shawn Standefer - 2023 - Review of Symbolic Logic 16 (4):1120-1157.
    We present a new frame semantics for positive relevant and substructural propositional logics. This frame semantics is both a generalisation of Routley–Meyer ternary frames and a simplification of them. The key innovation of this semantics is the use of a single accessibility relation to relate collections of points to points. Different logics are modeled by varying the kinds of collections used: they can be sets, multisets, lists or trees. We show that collection frames on trees are sound and complete for (...)
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  13. Proofnets for S5: sequents and circuits for modal logic.Greg Restall - 2007 - In C. Dimitracopoulos, L. Newelski & D. Normann (eds.), Logic Colloquium 2005: Proceedings of the Annual European Summer Meeting of the Association for Symbolic Logic, Held in Athens, Greece, July 28-August 3, 2005. Cambridge: Cambridge University Press. pp. 151-172.
    In this paper I introduce a sequent system for the propositional modal logic S5. Derivations of valid sequents in the system are shown to correspond to proofs in a novel natural deduction system of circuit proofs (reminiscient of proofnets in linear logic, or multiple-conclusion calculi for classical logic). -/- The sequent derivations and proofnets are both simple extensions of sequents and proofnets for classical propositional logic, in which the new machinery—to take account of the modal (...)
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  14. Approximating trees as coloured linear orders and complete axiomatisations of some classes of trees.Ruaan Kellerman & Valentin Goranko - 2021 - Journal of Symbolic Logic 86 (3):1035-1065.
    We study the first-order theories of some natural and important classes of coloured trees, including the four classes of trees whose paths have the order type respectively of the natural numbers, the integers, the rationals, and the reals. We develop a technique for approximating a tree as a suitably coloured linear order. We then present the first-order theories of certain classes of coloured linear orders and use them, along with the approximating technique, to establish complete axiomatisations of the (...)
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  15. Remarks on logic for process descriptions in ontological reasoning: A Drug Interaction Ontology case study.Mitsuhiro Okada, Barry Smith & Yutaro Sugimoto - 2008 - In Okada Mitsuhiro, Smith Barry & Sugimoto Yutaro (eds.), InterOntology. Proceedings of the First Interdisciplinary Ontology Meeting, Tokyo, Japan, 26-27 February 2008. Tokyo: Keio University Press. pp. 127-138.
    We present some ideas on logical process descriptions, using relations from the DIO (Drug Interaction Ontology) as examples and explaining how these relations can be naturally decomposed in terms of more basic structured logical process descriptions using terms from linear logic. In our view, the process descriptions are able to clarify the usual relational descriptions of DIO. In particular, we discuss the use of logical process descriptions in proving linear logical theorems. Among the types of reasoning supported (...)
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  16. Follow the Math!: The Mathematics of Quantum Mechanics as the Mathematics of Set Partitions Linearized to (Hilbert) Vector Spaces.David Ellerman - 2022 - Foundations of Physics 52 (5):1-40.
    The purpose of this paper is to show that the mathematics of quantum mechanics is the mathematics of set partitions linearized to vector spaces, particularly in Hilbert spaces. That is, the math of QM is the Hilbert space version of the math to describe objective indefiniteness that at the set level is the math of partitions. The key analytical concepts are definiteness versus indefiniteness, distinctions versus indistinctions, and distinguishability versus indistinguishability. The key machinery to go from indefinite to more definite (...)
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  17. Classes and theories of trees associated with a class of linear orders.Valentin Goranko & Ruaan Kellerman - 2011 - Logic Journal of the IGPL 19 (1):217-232.
    Given a class of linear order types C, we identify and study several different classes of trees, naturally associated with C in terms of how the paths in those trees are related to the order types belonging to C. We investigate and completely determine the set-theoretic relationships between these classes of trees and between their corresponding first-order theories. We then obtain some general results about the axiomatization of the first-order theories of some of these classes of trees in terms (...)
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  18. A New Logic, a New Information Measure, and a New Information-Based Approach to Interpreting Quantum Mechanics.David Ellerman - 2024 - Entropy Special Issue: Information-Theoretic Concepts in Physics 26 (2).
    The new logic of partitions is dual to the usual Boolean logic of subsets (usually presented only in the special case of the logic of propositions) in the sense that partitions and subsets are category-theoretic duals. The new information measure of logical entropy is the normalized quantitative version of partitions. The new approach to interpreting quantum mechanics (QM) is showing that the mathematics (not the physics) of QM is the linearized Hilbert space version of the mathematics of (...)
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  19. Judgement aggregation in non-classical logics.Daniele Porello - 2017 - Journal of Applied Non-Classical Logics 27 (1-2):106-139.
    This work contributes to the theory of judgement aggregation by discussing a number of significant non-classical logics. After adapting the standard framework of judgement aggregation to cope with non-classical logics, we discuss in particular results for the case of Intuitionistic Logic, the Lambek calculus, Linear Logic and Relevant Logics. The motivation for studying judgement aggregation in non-classical logics is that they offer a number of modelling choices to represent agents’ reasoning in aggregation problems. By studying judgement aggregation (...)
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  20. On an Intuitionistic Logic for Pragmatics.Gianluigi Bellin, Massimiliano Carrara & Daniele Chiffi - 2018 - Journal of Logic and Computation 50 (28):935–966..
    We reconsider the pragmatic interpretation of intuitionistic logic [21] regarded as a logic of assertions and their justi cations and its relations with classical logic. We recall an extension of this approach to a logic dealing with assertions and obligations, related by a notion of causal implication [14, 45]. We focus on the extension to co-intuitionistic logic, seen as a logic of hypotheses [8, 9, 13] and on polarized bi-intuitionistic logic as a (...) of assertions and conjectures: looking at the S4 modal translation, we give a de nition of a system AHL of bi-intuitionistic logic that correctly represents the duality between intuitionistic and co-intuitionistic logic, correcting a mistake in previous work [7, 10]. A computational interpretation of cointuitionism as a distributed calculus of coroutines is then used to give an operational interpretation of subtraction.Work on linear co-intuitionism is then recalled, a linear calculus of co-intuitionistic coroutines is de ned and a probabilistic interpretation of linear co-intuitionism is given as in [9]. Also we remark that by extending the language of intuitionistic logic we can express the notion of expectation, an assertion that in all situations the truth of p is possible and that in a logic of expectations the law of double negation holds. Similarly, extending co-intuitionistic logic, we can express the notion of conjecture that p, de ned as a hypothesis that in some situation the truth of p is epistemically necessary. (shrink)
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  21. The Dialectica Categories.Valeria Correa Vaz De Paiva - 1990 - Dissertation, University of Cambridge, Uk
    This thesis describes two classes of Dialectica categories. Chapter one introduces dialectica categories based on Goedel's Dialectica interpretation and shows that they constitute a model of Girard's Intuitionistic Linear Logic. Chapter two shows that, with extra assumptions, we can provide a comonad that interprets Girard's !-course modality. Chapter three presents the second class of Dialectica categories, a simplification suggested by Girard, that models (classical) Linear Logic and chapter four shows how to provide modalities ! and ? (...)
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  22. Logical consequence in modal logic II: Some semantic systems for S4.George Weaver - 1974 - Notre Dame Journal of Formal Logic 15:370.
    ABSTRACT: This 1974 paper builds on our 1969 paper (Corcoran-Weaver [2]). Here we present three (modal, sentential) logics which may be thought of as partial systematizations of the semantic and deductive properties of a sentence operator which expresses certain kinds of necessity. The logical truths [sc. tautologies] of these three logics coincide with one another and with those of standard formalizations of Lewis's S5. These logics, when regarded as logistic systems (cf. Corcoran [1], p. 154), are seen to be equivalent; (...)
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  23. Logical model of Personality and Cognition with possible Applications.Miro Brada - 2016 - In Park Woosuk (ed.), KAIST/KSBS International Workshop. KAIST. pp. 89-100.
    Although the cognition is significant in strategic reasoning, its role has been weakly analyzed, because only the average intelligence is usually considered. For example, prisoner's dilemma in game theory, would have different outcomes for persons with different intelligence. I show how various levels of intelligence influence the quality of reasoning, decision, or the probability of psychosis. I explain my original methodology developed for my MA thesis in clinical psychology in 1998, and grant research in 1999, demonstrating the bias of the (...)
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  24. Incompatibility Semantics from Agreement.Daniele Porello - 2012 - Philosophia 40 (1):99-119.
    In this paper, I discuss the analysis of logic in the pragmatic approach recently proposed by Brandom. I consider different consequence relations, formalized by classical, intuitionistic and linear logic, and I will argue that the formal theory developed by Brandom, even if provides powerful foundational insights on the relationship between logic and discursive practices, cannot account for important reasoning patterns represented by non-monotonic or resource-sensitive inferences. Then, I will present an incompatibility semantics in the framework of (...)
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  25. Commentary and Illocutionary Expressions in Linear Calculi of Natural Deduction.Moritz Cordes & Friedrich Reinmuth - 2017 - Logic and Logical Philosophy 26 (2).
    We argue that the need for commentary in commonly used linear calculi of natural deduction is connected to the “deletion” of illocutionary expressions that express the role of propositions as reasons, assumptions, or inferred propositions. We first analyze the formalization of an informal proof in some common calculi which do not formalize natural language illocutionary expressions, and show that in these calculi the formalizations of the example proof rely on commentary devices that have no counterpart in the original proof. (...)
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  26. Neutrosophic Treatment of the Modified Simplex Algorithm to find the Optimal Solution for Linear Models.Maissam Jdid & Florentin Smarandache - 2023 - International Journal of Neutrosophic Science 23.
    Science is the basis for managing the affairs of life and human activities, and living without knowledge is a form of wandering and a kind of loss. Using scientific methods helps us understand the foundations of choice, decision-making, and adopting the right solutions when solutions abound and options are numerous. Operational research is considered the best that scientific development has provided because its methods depend on the application of scientific methods in solving complex issues and the optimal use of available (...)
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  27. Lineales.Martin Hyland & Valeria de Paiva - 1991 - O Que Nos Faz Pensar:107-123.
    The first aim of this note is to describe an algebraic structure, more primitive than lattices and quantales, which corresponds to the intuitionistic flavour of Linear Logic we prefer. This part of the note is a total trivialisation of ideas from category theory and we play with a toy-structure a not distant cousin of a toy-language. The second goal of the note is to show a generic categorical construction, which builds models for Linear Logic, similar to (...)
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  28. A proof-theoretical view of collective rationality.Daniele Porello - 2013 - In Proceedings of the 23rd International Joint Conference of Artificial Intelligence (IJCAI 2013).
    The impossibility results in judgement aggregation show a clash between fair aggregation procedures and rational collective outcomes. In this paper, we are interested in analysing the notion of rational outcome by proposing a proof-theoretical understanding of collective rationality. In particular, we use the analysis of proofs and inferences provided by linear logic in order to define a fine-grained notion of group reasoning that allows for studying collective rationality with respect to a number of logics. We analyse the well-known (...)
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  29. Propositional interval neighborhood logics: Expressiveness, decidability, and undecidable extensions.Davide Bresolin, Valentin Goranko, Angelo Montanari & Guido Sciavicco - 2010 - Annals of Pure and Applied Logic 161 (3):289-304.
    In this paper, we investigate the expressiveness of the variety of propositional interval neighborhood logics , we establish their decidability on linearly ordered domains and some important subclasses, and we prove the undecidability of a number of extensions of PNL with additional modalities over interval relations. All together, we show that PNL form a quite expressive and nearly maximal decidable fragment of Halpern–Shoham’s interval logic HS.
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  30. Aristotle and Linearity in Substance, Measure, and Motion.Paul Taborsky - 2022 - Axiomathes 32 (6):1375-1399.
    The model of a closed linear measure space, which can be used to model Aristotle’s treatment of motion (kinesis), can be analogically extended to the qualitative ‘spaces’ implied by his theory of contraries in Physics I and in Metaphysics Iota, and to the dimensionless ‘space’ of the unity of matter and form discussed in book Eta of the Metaphysics. By examining Aristotle’s remarks on contraries, the subject of change, continuity, and the unity of matter and form, Aristotle’s thoughts on (...)
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  31. METAPHYSICAL RELATIVITY THEORY I: M-LOGIC.Eric Hahn - manuscript
    The present text provides a logical theory which originated in the unification of a number of well-known philosophical logics as well as the introduction and study of new operators. Further M-logic contains an object theory. With both the logical part and the object part we achieve a formal calculus that is able to express many metaphysical dogmas.
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  32. Notes on the Model Theory of DeMorgan Logics.Thomas Macaulay Ferguson - 2012 - Notre Dame Journal of Formal Logic 53 (1):113-132.
    We here make preliminary investigations into the model theory of DeMorgan logics. We demonstrate that Łoś's Theorem holds with respect to these logics and make some remarks about standard model-theoretic properties in such contexts. More concretely, as a case study we examine the fate of Cantor's Theorem that the classical theory of dense linear orderings without endpoints is $\aleph_{0}$-categorical, and we show that the taking of ultraproducts commutes with respect to previously established methods of constructing nonclassical structures, namely, Priest's (...)
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  33. Tensed Ontology Based on Simple Partial Logic.Daisuke Kachi - 2002 - Proceedings of Ninth International Symposium on Temporal Representation and Reasoning: TIME-02:141-145.
    Simple partial logic (=SPL) is, broadly speaking, an extensional logic which allows for the truth-value gap. First I give a system of propositional SPL by partializing classical logic, as well as extending it with several non-classical truth-functional operators. Second I show a way based on SPL to construct a system of tensed ontology, by representing tensed statements as two kinds of necessary statements in a linear model that consists of the present and future worlds. Finally I (...)
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  34. Logical Types in Quantum Mechanics.Andrew Soltau - manuscript
    Barbour shows that time does not exist in the physical world, and similar conclusions are reached by others such as Deutsch, Davies and Woodward. Every possible configuration of a physical environment simply exists in the universe. The system is objectively static. Observation, however, is an inherently transtemporal phenomenon, involving actual or effective change of the configuration, collapse. Since, in a static environment, all possible configurations exist, transtemporal reality is of the logical type of a movie. The frame of a movie (...)
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  35. Incompleteness of a first-order Gödel logic and some temporal logics of programs.Matthias Baaz, Alexander Leitsch & Richard Zach - 1996 - In Kleine Büning Hans (ed.), Computer Science Logic. CSL 1995. Selected Papers. Springer. pp. 1--15.
    It is shown that the infinite-valued first-order Gödel logic G° based on the set of truth values {1/k: k ε w {0}} U {0} is not r.e. The logic G° is the same as that obtained from the Kripke semantics for first-order intuitionistic logic with constant domains and where the order structure of the model is linear. From this, the unaxiomatizability of Kröger's temporal logic of programs (even of the fragment without the nexttime operator O) (...)
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  36. Kripke Semantics for Fuzzy Logics.Saeed Salehi - 2018 - Soft Computing 22 (3):839–844.
    Kripke frames (and models) provide a suitable semantics for sub-classical logics; for example, intuitionistic logic (of Brouwer and Heyting) axiomatizes the reflexive and transitive Kripke frames (with persistent satisfaction relations), and the basic logic (of Visser) axiomatizes transitive Kripke frames (with persistent satisfaction relations). Here, we investigate whether Kripke frames/models could provide a semantics for fuzzy logics. For each axiom of the basic fuzzy logic, necessary and sufficient conditions are sought for Kripke frames/models which satisfy them. It (...)
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  37. A general tableau method for propositional interval temporal logics: Theory and implementation.V. Goranko, A. Montanari, P. Sala & G. Sciavicco - 2006 - Journal of Applied Logic 4 (3):305-330.
    In this paper we focus our attention on tableau methods for propositional interval temporal logics. These logics provide a natural framework for representing and reasoning about temporal properties in several areas of computer science. However, while various tableau methods have been developed for linear and branching time point-based temporal logics, not much work has been done on tableau methods for interval-based ones. We develop a general tableau method for Venema's \cdt\ logic interpreted over partial orders (\nsbcdt\ for short). (...)
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  38. Times two: The tenses of linear and collapse dynamics in relational quantum mechanics.Andrew Soltau - manuscript
    The nature and topology of time remains an open question in philosophy, both tensed and tenseless concepts of time appear to have merit. A concept of time including both kinds of time evolution of physical systems in quantum mechanics subsumes the properties of both notions. The linear dynamics defines the universe probabilistically throughout space-time, and can be seen as the definition of a block universe. The collapse dynamics is the time evolution of the linear dynamics, and is thus (...)
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  39. Language, Lambdas, and Logic.Reinhard Muskens - 2003 - In R. Oehrle & J. Kruijff (eds.), resource sensitivity, binding, and anaphora. kluwer. pp. 23--54.
    The paper develops Lambda Grammars, a form of categorial grammar that, unlike other categorial formalisms, is non-directional. Linguistic signs are represented as sequences of lambda terms and are combined with the help of linear combinators.
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  40. Generation of Biological Patterns and Form: Some Physical, Mathematical and Logical Aspects.Alfred Gierer - 1981 - Progress in Biophysics and Molecular Biology 37 (1):1-48.
    While many different mechanisms contribute to the generation of spatial order in biological development, the formation of morphogenetic fields which in turn direct cell responses giving rise to pattern and form are of major importance and essential for embryogenesis and regeneration. Most likely the fields represent concentration patterns of substances produced by molecular kinetics. Short range autocatalytic activation in conjunction with longer range “lateral” inhibition or depletion effects is capable of generating such patterns (Gierer and Meinhardt, 1972). Non-linear reactions (...)
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  41. Completeness of a first-order temporal logic with time-gaps.Matthias Baaz, Alexander Leitsch & Richard Zach - 1996 - Theoretical Computer Science 160 (1-2):241-270.
    The first-order temporal logics with □ and ○ of time structures isomorphic to ω (discrete linear time) and trees of ω-segments (linear time with branching gaps) and some of its fragments are compared: the first is not recursively axiomatizable. For the second, a cut-free complete sequent calculus is given, and from this, a resolution system is derived by the method of Maslov.
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  42. Towards Tractable Approximations to Many-Valued Logics: the Case of First Degree Entailment.Alejandro Solares-Rojas & Marcello D’Agostino - 2022 - In Igor Sedlár (ed.), The Logica Yearbook 2021. College Publications. pp. 57-76.
    FDE is a logic that captures relevant entailment between implication-free formulae and admits of an intuitive informational interpretation as a 4-valued logic in which “a computer should think”. However, the logic is co-NP complete, and so an idealized model of how an agent can think. We address this issue by shifting to signed formulae where the signs express imprecise values associated with two distinct bipartitions of the set of standard 4 values. Thus, we present a proof system (...)
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  43. The World Hologram: The Holographic Universe is Everett's Relative State - The Measurement Problem is a Category Error of Logical Type.Andrew Soltau - manuscript
    The key to the measurement problem is the entity at the heart of Everett's formulation, the state of the memory, defined as the record of observations. In humans, the integrated synthesis defines the perceptual reality, a projective, three-dimensional representation of the world. This 'world hologram' is the conscious point of view, the mind in Lockwood's interpretation, the 'phenomenal perspective'. As Everett demonstrates, the collapse dynamics operates only judged by the state of the memory; the physical observer remains in a superposed (...)
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  44. Lambda Grammars and the Syntax-Semantics Interface.Reinhard Muskens - 2001 - In Robert Van Rooij & Martin Stokhof (eds.), Proceedings of the Thirteenth Amsterdam Colloquium. Amsterdam: ILLC. pp. 150-155.
    In this paper we discuss a new perspective on the syntax-semantics interface. Semantics, in this new set-up, is not ‘read off’ from Logical Forms as in mainstream approaches to generative grammar. Nor is it assigned to syntactic proofs using a Curry-Howard correspondence as in versions of the Lambek Calculus, or read off from f-structures using Linear Logic as in Lexical-Functional Grammar (LFG, Kaplan & Bresnan [9]). All such approaches are based on the idea that syntactic objects (trees, proofs, (...)
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  45. Categorial Grammar and Lexical-Functional Grammar.Reinhard Muskens - 2001 - In Miriam Butt & Tracey Holloway King (eds.), Proceedings of the LFG01 Conference, University of Hong Kong. CSLI Publications. pp. 259-279.
    This paper introduces λ-grammar, a form of categorial grammar that has much in common with LFG. Like other forms of categorial grammar, λ-grammars are multi-dimensional and their components are combined in a strictly parallel fashion. Grammatical representations are combined with the help of linear combinators, closed pure λ-terms in which each abstractor binds exactly one variable. Mathematically this is equivalent to employing linear logic, in use in LFG for semantic composition, but the method seems more practicable.
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  46. Theoremizing Yablo's Paradox.Ahmad Karimi & Saeed Salehi - manuscript
    To counter a general belief that all the paradoxes stem from a kind of circularity (or involve some self--reference, or use a diagonal argument) Stephen Yablo designed a paradox in 1993 that seemingly avoided self--reference. We turn Yablo's paradox, the most challenging paradox in the recent years, into a genuine mathematical theorem in Linear Temporal Logic (LTL). Indeed, Yablo's paradox comes in several varieties; and he showed in 2004 that there are other versions that are equally paradoxical. Formalizing (...)
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  47. Perceptron Connectives in Knowledge Representation.Pietro Galliani, Guendalina Righetti, Daniele Porello, Oliver Kutz & Nicolas Toquard - 2020 - In Pietro Galliani, Guendalina Righetti, Daniele Porello, Oliver Kutz & Nicolas Toquard (eds.), Knowledge Engineering and Knowledge Management - 22nd International Conference, {EKAW} 2020, Bolzano, Italy, September 16-20, 2020, Proceedings. Lecture Notes in Computer Science 12387. pp. 183-193.
    We discuss the role of perceptron (or threshold) connectives in the context of Description Logic, and in particular their possible use as a bridge between statistical learning of models from data and logical reasoning over knowledge bases. We prove that such connectives can be added to the language of most forms of Description Logic without increasing the complexity of the corresponding inference problem. We show, with a practical example over the Gene Ontology, how even simple instances of perceptron (...)
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  48.  95
    Neutrosophic Transport and Assignment Issues.Florentin Smarandache - 2023 - Infinite Study.
    We all know that problems of transportation and allocation appear frequently in practical life. We need to transfer materials from production centers to consumption centers to secure the areas’ need for the transported material or allocate machines or people to do a specific job at the lowest cost, or in the shortest time. We know that the cost factors Time is one of the most important factors that decision-makers care about because it plays an “important” role in many of the (...)
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  49. Diagonal arguments and fixed points.Saeed Salehi - 2017 - Bulletin of the Iranian Mathematical Society 43 (5):1073-1088.
    ‎A universal schema for diagonalization was popularized by N. S‎. ‎Yanofsky (2003)‎, ‎based on a pioneering work of F.W‎. ‎Lawvere (1969)‎, ‎in which the existence of a (diagonolized-out and contradictory) object implies the existence of a fixed-point for a certain function‎. ‎It was shown that many self-referential paradoxes and diagonally proved theorems can fit in that schema‎. ‎Here‎, ‎we fit more theorems in the universal‎ ‎schema of diagonalization‎, ‎such as Euclid's proof for the infinitude of the primes and new proofs (...)
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  50. Combinatoriality and Compositionality in Everyday Primate Skills.Nathalie Gontier - forthcoming - International Journal of Primatology.
    Human language, hominin tool production modes, and multimodal communications systems of primates and other animals are currently well-studied for how they display compositionality or combinatoriality. In all cases, the former is defined as a kind of hierarchical nesting and the latter as a lack thereof. In this article, I extend research on combinatoriality and compositionality further to investigations of everyday primate skills. Daily locomotion modes as well as behaviors associated with subsistence practices, hygiene, or body modification rely on the hierarchical (...)
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