Results for 'Intermediate Logics'

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  1. Epsilon theorems in intermediate logics.Matthias Baaz & Richard Zach - 2022 - Journal of Symbolic Logic 87 (2):682-720.
    Any intermediate propositional logic can be extended to a calculus with epsilon- and tau-operators and critical formulas. For classical logic, this results in Hilbert’s $\varepsilon $ -calculus. The first and second $\varepsilon $ -theorems for classical logic establish conservativity of the $\varepsilon $ -calculus over its classical base logic. It is well known that the second $\varepsilon $ -theorem fails for the intuitionistic $\varepsilon $ -calculus, as prenexation is impossible. The paper investigates the effect of adding critical $\varepsilon $ (...)
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  2. Intermediate Logics and the de Jongh property.Dick de Jongh, Rineke Verbrugge & Albert Visser - 2011 - Archive for Mathematical Logic 50 (1-2):197-213.
    We prove that all extensions of Heyting Arithmetic with a logic that has the finite frame property possess the de Jongh property.
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  3. Intermediate Logics and the de Jongh property.Dick Jongh, Rineke Verbrugge & Albert Visser - 2011 - Archive for Mathematical Logic 50 (1-2):197-213.
    We prove that all extensions of Heyting Arithmetic with a logic that has the finite frame property possess the de Jongh property.
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  4. Polyhedral Completeness of Intermediate Logics: The Nerve Criterion.Sam Adam-day, Nick Bezhanishvili, David Gabelaia & Vincenzo Marra - 2024 - Journal of Symbolic Logic 89 (1):342-382.
    We investigate a recently devised polyhedral semantics for intermediate logics, in which formulas are interpreted in n-dimensional polyhedra. An intermediate logic is polyhedrally complete if it is complete with respect to some class of polyhedra. The first main result of this paper is a necessary and sufficient condition for the polyhedral completeness of a logic. This condition, which we call the Nerve Criterion, is expressed in terms of Alexandrov’s notion of the nerve of a poset. It affords (...)
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  5. Cartesian Dualism and the Intermediate State: A Reply to Turner Jr.Alejandro Pérez - 2019 - Forum: Supplement to Acta Philosophica 5 (1):269-281.
    In this paper, I propose to analyse two objections raised by Turner Jr in his paper “On Two Reasons Christian Theologians Should Reject The Intermediate State” in order to show that the intermediate state is an incoherent theory. As we shall see, the two untoward consequences that he mentions do not imply a metaphysical or logical contradiction. Consequently, I shall defend an Intermediate State and I shall propose briefly one metaphysical conception of the human being able to (...)
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  6. Aristotle's demonstrative logic.John Corcoran - 2009 - History and Philosophy of Logic 30 (1):1-20.
    Demonstrative logic, the study of demonstration as opposed to persuasion, is the subject of Aristotle's two-volume Analytics. Many examples are geometrical. Demonstration produces knowledge (of the truth of propositions). Persuasion merely produces opinion. Aristotle presented a general truth-and-consequence conception of demonstration meant to apply to all demonstrations. According to him, a demonstration, which normally proves a conclusion not previously known to be true, is an extended argumentation beginning with premises known to be truths and containing a chain of reasoning showing (...)
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  7. Buying Logical Principles with Ontological Coin: The Metaphysical Lessons of Adding epsilon to Intuitionistic Logic.David DeVidi & Corey Mulvihill - 2017 - IfCoLog Journal of Logics and Their Applications 4 (2):287-312.
    We discuss the philosophical implications of formal results showing the con- sequences of adding the epsilon operator to intuitionistic predicate logic. These results are related to Diaconescu’s theorem, a result originating in topos theory that, translated to constructive set theory, says that the axiom of choice (an “existence principle”) implies the law of excluded middle (which purports to be a logical principle). As a logical choice principle, epsilon allows us to translate that result to a logical setting, where one can (...)
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  8. Existence Assumptions and Logical Principles: Choice Operators in Intuitionistic Logic.Corey Edward Mulvihill - 2015 - Dissertation, University of Waterloo
    Hilbert’s choice operators τ and ε, when added to intuitionistic logic, strengthen it. In the presence of certain extensionality axioms they produce classical logic, while in the presence of weaker decidability conditions for terms they produce various superintuitionistic intermediate logics. In this thesis, I argue that there are important philosophical lessons to be learned from these results. To make the case, I begin with a historical discussion situating the development of Hilbert’s operators in relation to his evolving program (...)
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  9. Many-Valued And Fuzzy Logic Systems From The Viewpoint Of Classical Logic.Ekrem Sefa Gül - 2018 - Tasavvur - Tekirdag Theology Journal 4 (2):624 - 657.
    The thesis that the two-valued system of classical logic is insufficient to explanation the various intermediate situations in the entity, has led to the development of many-valued and fuzzy logic systems. These systems suggest that this limitation is incorrect. They oppose the law of excluded middle (tertium non datur) which is one of the basic principles of classical logic, and even principle of non-contradiction and argue that is not an obstacle for things both to exist and to not exist (...)
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  10. Natural Deduction for Three-Valued Regular Logics.Yaroslav Petrukhin - 2017 - Logic and Logical Philosophy 26 (2):197–206.
    In this paper, I consider a family of three-valued regular logics: the well-known strong and weak S.C. Kleene’s logics and two intermedi- ate logics, where one was discovered by M. Fitting and the other one by E. Komendantskaya. All these systems were originally presented in the semantical way and based on the theory of recursion. However, the proof theory of them still is not fully developed. Thus, natural deduction sys- tems are built only for strong Kleene’s logic (...)
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  11. Bourne on future contingents and three-valued logic.Daisuke Kachi - 2009 - Logic and Logical Philosophy 18 (1):33-43.
    Recently, Bourne constructed a system of three-valued logic that he supposed to replace Łukasiewicz’s three-valued logic in view of the problems of future contingents. In this paper, I will show first that Bourne’s system makes no improvement to Łukasiewicz’s system. However, finding some good motivations and lessons in his attempt, next I will suggest a better way of achieving his original goal in some sense. The crucial part of my way lies in reconsidering the significance of the intermediate truth-value (...)
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  12. A generic Solution to the Sorites Paradox.Susanne Bobzien - 2024 - Erkenntnis 2024 (Online):1-40.
    ABSTRACT: This paper offers a generic revenge-proof solution to the Sorites paradox that is compatible with several philosophical approaches to vagueness, including epistemicism, supervaluationism, psychological contextualism and intuitionism. The solution is traditional in that it rejects the Sorites conditional and proposes a modally expressed weakened conditional instead. The modalities are defined by the first-order logic QS4M+FIN. (This logic is a modal companion to the intermediate logic QH+KF, which places the solution between intuitionistic and classical logic.) Borderlineness is introduced modally (...)
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  13. To reply or not to reply, that is the question: descriptive metaphysics and the sceptical challenge.Giuseppina D'Oro - 2023 - In Benjamin De Mesel and Sybren Heyndels Audun Bengtson (ed.), P.F. Strawson and His Philosophical Legacy. Oxford University Press. pp. 192-211.
    How should one respond to scepticism? Should one seek to refute it? Or should scepticism be ignored? This paper argues that descriptive metaphysics occupies an intermediate logical space between truth-directed transcendental arguments aimed at refuting the sceptic and the quietist stance of the Humean naturalist who declines to take up the sceptical challenge. Descriptive metaphysics is neither quietist nor confrontational. It seeks to show, rather, that the sceptic is not a genuine partner in conversation.
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  14.  97
    (1 other version)Question-relative knowledge for minimally rational agents.Francisca Silva - 2024 - Inquiry: An Interdisciplinary Journal of Philosophy:1-31.
    Agents know some but not all logical consequences of what they know. Agents seem to be neither logically omniscient nor logically incompetent. Yet finding an intermediate standard of minimal rationality has proven difficult. In this paper, I take suggestions found in the literature (Lewis, 1988; Hawke, Özgün and Berto, 2020; Plebani and Spolaore, 2021) and join the forces of subject matter and impossible worlds approaches to devise a new solution to this quandary. I do so by combining a space (...)
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  15. Working Backwards with Copi's Inference Rules.Robert Allen - 1996 - American Philosophical Association Journal on Teaching Philosophy 95 (Spring):103-104.
    In their Introduction to Logic, Copi and Cohen suggest that students construct a formal proof by "working backwards from the conclusion by looking for some statement or statements from which it can be deduced and then trying to deduce those intermediate statements from the premises. What follows is an elaboration of this suggestion. I describe an almost mechanical procedure for determining from which statement(s) the conclusion can be deduced and the rules by which the required inferences can be made. (...)
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  16. (1 other version)Nagel’s Philosophical Development.Sander Verhaegh - 2021 - In Matthias Neuber & Adam Tamas Tuboly (eds.), Ernest Nagel: Philosophy of Science and the Fight for Clarity. Springer. pp. 43-65.
    Ernest Nagel played a key role in bridging the gap between American philosophy and logical empiricism. He introduced European philosophy of science to the American philosophical community but also remained faithful to the naturalism of his teachers. This paper aims to shed new light on Nagel’s intermediating endeavors by reconstructing his philosophical development in the late 1920s and 1930s. This is a decisive period in Nagel’s career because it is the phase in which he first formulated the principles of his (...)
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  17. Actions and Events in Plural Discourse.Kirk Ludwig - 2016 - In Kirk Ludwig & Marija Jankovic (eds.), The Routledge Handbook of Collective Intentionality. New York: Routledge. pp. 476-488.
    This chapter is concerned with plural discourse in the grammatical sense. The goal of the chapter is to urge the value of the event analysis of the matrix of action sentences in thinking about logical form in plural discourse about action. Among the claims advanced are that: -/- 1. The ambiguity between distributive and collective readings of plural action sentences is not lexical ambiguity, either in the noun phrase (NP) or in the verb phrase (VP), but an ambiguity tracing to (...)
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  18. REVIEW OF 1988. Saccheri, G. Euclides Vindicatus (1733), edited and translated by G. B. Halsted, 2nd ed. (1986), in Mathematical Reviews MR0862448. 88j:01013.John Corcoran - 1988 - MATHEMATICAL REVIEWS 88 (J):88j:01013.
    Girolamo Saccheri (1667--1733) was an Italian Jesuit priest, scholastic philosopher, and mathematician. He earned a permanent place in the history of mathematics by discovering and rigorously deducing an elaborate chain of consequences of an axiom-set for what is now known as hyperbolic (or Lobachevskian) plane geometry. Reviewer's remarks: (1) On two pages of this book Saccheri refers to his previous and equally original book Logica demonstrativa (Turin, 1697) to which 14 of the 16 pages of the editor's "Introduction" are devoted. (...)
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  19. Structural Relativity and Informal Rigour.Neil Barton - 2022 - In Gianluigi Oliveri, Claudio Ternullo & Stefano Boscolo (eds.), Objects, Structures, and Logics, FilMat Studies in the Philosophy of Mathematics. Springer. pp. 133-174.
    Informal rigour is the process by which we come to understand particular mathematical structures and then manifest this rigour through axiomatisations. Structural relativity is the idea that the kinds of structures we isolate are dependent upon the logic we employ. We bring together these ideas by considering the level of informal rigour exhibited by our set-theoretic discourse, and argue that different foundational programmes should countenance different underlying logics (intermediate between first- and second-order) for formulating set theory. By bringing (...)
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  20. Fuzziness and the sorites paradox.Marcelo Vasconez - 2006 - Dissertation, Catholic University of Louvain
    The dissertation has two parts, each dealing with a problem, namely: 1) What is the most adequate account of fuzziness -the so-called phenomenon of vagueness?, and 2) what is the most plausible solution to the sorites, or heap paradox? I will try to show that fuzzy properties are those which are gradual, amenable to be possessed in a greater or smaller extent. Acknowledgement of degrees in the instantiation of a property allows for a gradual transition from one opposite to the (...)
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  21. 4. Contradictorial Gradualism Vs. Discontinuism: Two Views On Fuzziness And The Transition Problem.Marcelo VÁsconez - 2006 - Logique Et Analyse 49 (195).
    The dissertation has two parts, each dealing with a problem, namely: 1) What is the most adequate account of fuzziness -the so-called phenomenon of vagueness?, and 2) what is the most plausible solution to the sorites, or heap paradox? I will try to show that fuzzy properties are those which are gradual, amenable to be possessed in a greater or smaller extent. Acknowledgement of degrees in the instantiation of a property allows for a gradual transition from one opposite to the (...)
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  22.  51
    Model for ensuring business excellence on the basis of management innovation.Igor Kryvovyazyuk - 2022 - Economic Forum 1 (2):112-119.
    The problem of building an effective system of interconnected and purposeful innovative changes in business management is solved in the article. The main purpose of the research is to improve the model of business excellence on the basis of interconnected and purposeful innovative changes in business management. Critical analysis of literature sources and approaches to solving the problem of building a perfect model of business emphasizes the diversity of applied methodological approaches and methods of management innovation. However, in terms of (...)
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  23. Ambiguity Aversion behind the Veil of Ignorance.H. Orri Stefánsson - 2021 - Synthese 198 (7):6159-6182.
    The veil of ignorance argument was used by John C. Harsanyi to defend Utilitarianism and by John Rawls to defend the absolute priority of the worst off. In a recent paper, Lara Buchak revives the veil of ignorance argument, and uses it to defend an intermediate position between Harsanyi's and Rawls' that she calls Relative Prioritarianism. None of these authors explore the implications of allowing that agent's behind the veil are averse to ambiguity. Allowing for aversion to ambiguity---which is (...)
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  24. Evolution in Space and Time: The Second Synthesis of Ecology, Evolutionary Biology, and the Philosophy of Biology.Mitchell Ryan Distin - 2023 - Self-published because fuck the leeches of Big Publishing.
    Change is the fundamental idea of evolution. Explaining the extraordinary biological change we see written in the history of genomes and fossil beds is the primary occupation of the evolutionary biologist. Yet it is a surprising fact that for the majority of evolutionary research, we have rarely studied how evolution typically unfolds in nature, in changing ecological environments, over space and time. While ecology played a major role in the eventual acceptance of the population genetic viewpoint of evolution in the (...)
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  25. On the possibility of stable regularities without fundamental laws.Aldo Filomeno - 2014 - Dissertation, Autonomous University of Barcelona
    This doctoral dissertation investigates the notion of physical necessity. Specifically, it studies whether it is possible to account for non-accidental regularities without the standard assumption of a pre-existent set of governing laws. Thus, it takes side with the so called deflationist accounts of laws of nature, like the humean or the antirealist. The specific aim is to complement such accounts by providing a missing explanation of the appearance of physical necessity. In order to provide an explanation, I recur to fields (...)
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  26. Near Closeness and Conditionals.Daniel Berntson - manuscript
    This paper presents a new system of conditional logic B2, which is strictly intermediate in strength between the existing systems B1 and B3 from John Burgess (1981) and David Lewis (1973a). After presenting and motivating the new system, we will show that it is characterized by a natural class of frames. These frames correspond to the idea that conditionals are about which worlds are nearly closest, rather than which worlds are closest. Along the way, we will also give new (...)
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  27. "Infinity, Knowledge, and Divinity in the Thought of Cusanus and Cantor" (Manuscript draft of first page of forthcoming book chapter ).Anne Newstead (ed.) - forthcoming - Berlin: De Gruyter.
    Renaissance philosopher, mathematician, and theologian Nicholas of Cusa (1401-1464) said that there is no proportion between the finite mind and the infinite. He is fond of saying reason cannot fully comprehend the infinite. That our best hope for attaining a vision and understanding of infinite things is by mathematics and by the use of contemplating symbols, which help us grasp "the absolute infinite". By the late 19th century, there is a decisive intervention in mathematics and its philosophy: the philosophical mathematician (...)
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  28. Absolute Infinity, Knowledge, and Divinity in the Thought of Cusanus and Cantor (ABSTRACT ONLY).Anne Newstead - 2024 - In Mirosław Szatkowski (ed.), Ontology of Divinity. De Gruyter. pp. 561-580.
    Renaissance philosopher, mathematician, and theologian Nicholas of Cusa (1401-1464) said that there is no proportion between the finite mind and the infinite. He is fond of saying reason cannot fully comprehend the infinite. That our best hope for attaining a vision and understanding of infinite things is by mathematics and by the use of contemplating symbols, which help us grasp "the absolute infinite". By the late 19th century, there is a decisive intervention in mathematics and its philosophy: the philosophical mathematician (...)
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  29. What the Tortoise Said to Achilles: Lewis Carroll’s paradox in terms of Hilbert arithmetic.Vasil Penchev - 2021 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 13 (22):1-32.
    Lewis Carroll, both logician and writer, suggested a logical paradox containing furthermore two connotations (connotations or metaphors are inherent in literature rather than in mathematics or logics). The paradox itself refers to implication demonstrating that an intermediate implication can be always inserted in an implication therefore postponing its ultimate conclusion for the next step and those insertions can be iteratively and indefinitely added ad lib, as if ad infinitum. Both connotations clear up links due to the shared formal (...)
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  30. Theories with the Independence Property, Studia Logica 2010 95:379-405.Mlj van de Vel - 2010 - Studia Logica 95 (3):379-405.
    A first-order theory T has the Independence Property provided deduction of a statement of type (quantifiers) (P -> (P1 or P2 or .. or Pn)) in T implies that (quantifiers) (P -> Pi) can be deduced in T for some i, 1 <= i <= n). Variants of this property have been noticed for some time in logic programming and in linear programming. We show that a first-order theory has the Independence Property for the class of basic formulas provided it (...)
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  31. From the four-color theorem to a generalizing “four-letter theorem”: A sketch for “human proof” and the philosophical interpretation.Vasil Penchev - 2020 - Logic and Philosophy of Mathematics eJournal (Elsevier: SSRN) 12 (21):1-10.
    The “four-color” theorem seems to be generalizable as follows. The four-letter alphabet is sufficient to encode unambiguously any set of well-orderings including a geographical map or the “map” of any logic and thus that of all logics or the DNA plan of any alive being. Then the corresponding maximally generalizing conjecture would state: anything in the universe or mind can be encoded unambiguously by four letters. That admits to be formulated as a “four-letter theorem”, and thus one can search (...)
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  32. (1 other version)The Concept of Genus in Aristotle.Mohammad Bagher Ghomi - manuscript
    We have a basic definition of genus in Topics (I, 5, 102a31-35): ‘A genus is what is predicated in what a thing is of a number of things exhibiting differences in kind. We should treat as predicate in what a thing is all such things as it would be appropriate to mention in reply to the question “what is the object in question?”; as, for example, in the case of man, if asked that question, it is appropriate to say “He (...)
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  33. L'etica del Novecento. Dopo Nietzsche.Sergio Cremaschi - 2005 - Roma RM, Italia: Carocci.
    TWENTIETH-CENTURY ETHICS. AFTER NIETZSCHE -/- Preface This book tells the story of twentieth-century ethics or, in more detail, it reconstructs the history of a discussion on the foundations of ethics which had a start with Nietzsche and Sidgwick, the leading proponents of late-nineteenth-century moral scepticism. During the first half of the century, the prevailing trends tended to exclude the possibility of normative ethics. On the Continent, the trend was to transform ethics into a philosophy of existence whose self-appointed task was (...)
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  34. Aristotle on the Relations between Genera, Species and Differentia.Mohammad Bagher Ghomi - manuscript
    The following are the characteristics of a genus: 1. Those to which the same figure of predication applies are one in genus. (Met. , Δ, 1016b32-35) 2. Things that are one in genus are all one by analogy while things that are one by analogy are not all one in genus. (Met, Δ, 1016b35-1017a3) 3. A genus includes contraries. (Met., Δ, 1018a25-31) 4. All the intermediates are in the same genus as one another and as the things they stand between. (...)
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  35. On the weak Kleene scheme in Kripke's theory of truth.James Cain & Zlatan Damnjanovic - 1991 - Journal of Symbolic Logic 56 (4):1452-1468.
    It is well known that the following features hold of AR + T under the strong Kleene scheme, regardless of the way the language is Gödel numbered: 1. There exist sentences that are neither paradoxical nor grounded. 2. There are 2ℵ0 fixed points. 3. In the minimal fixed point the weakly definable sets (i.e., sets definable as {n∣ A(n) is true in the minimal fixed point where A(x) is a formula of AR + T) are precisely the Π1 1 sets. (...)
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  36. Semantical analysis of weak Kleene logics.Roberto Ciuni & Massimiliano Carrara - 2019 - Journal of Applied Non-Classical Logics 29 (1):1-36.
    This paper presents a semantical analysis of the Weak Kleene Logics Kw3 and PWK from the tradition of Bochvar and Halldén. These are three-valued logics in which a formula takes the third value if at least one of its components does. The paper establishes two main results: a characterisation result for the relation of logical con- sequence in PWK – that is, we individuate necessary and sufficient conditions for a set.
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  37. Towards a philosophical understanding of the logics of formal inconsistency.Walter Carnielli & Abílio Rodrigues - 2015 - Manuscrito 38 (2):155-184.
    In this paper we present a philosophical motivation for the logics of formal inconsistency, a family of paraconsistent logics whose distinctive feature is that of having resources for expressing the notion of consistency within the object language in such a way that consistency may be logically independent of non-contradiction. We defend the view according to which logics of formal inconsistency may be interpreted as theories of logical consequence of an epistemological character. We also argue that in order (...)
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  38. Relating Semantics for Hyper-Connexive and Totally Connexive Logics.Jacek Malinowski & Ricardo Arturo Nicolás-Francisco - 2023 - Logic and Logical Philosophy (Special Issue: Relating Logic a):1-14.
    In this paper we present a characterization of hyper-connexivity by means of a relating semantics for Boolean connexive logics. We also show that the minimal Boolean connexive logic is Abelardian, strongly consistent, Kapsner strong and antiparadox. We give an example showing that the minimal Boolean connexive logic is not simplificative. This shows that the minimal Boolean connexive logic is not totally connexive.
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  39. LP, K3, and FDE as Substructural Logics.Lionel Shapiro - 2017 - In Arazim Pavel & Lávička Tomáš (eds.), The Logica Yearbook 2016. College Publications.
    Building on recent work, I present sequent systems for the non-classical logics LP, K3, and FDE with two main virtues. First, derivations closely resemble those in standard Gentzen-style systems. Second, the systems can be obtained by reformulating a classical system using nonstandard sequent structure and simply removing certain structural rules (relatives of exchange and contraction). I clarify two senses in which these logics count as “substructural.”.
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  40. The philosophy of alternative logics.Andrew Aberdein & Stephen Read - 2009 - In Leila Haaparanta (ed.), The development of modern logic. New York: Oxford University Press. pp. 613-723.
    This chapter focuses on alternative logics. It discusses a hierarchy of logical reform. It presents case studies that illustrate particular aspects of the logical revisionism discussed in the chapter. The first case study is of intuitionistic logic. The second case study turns to quantum logic, a system proposed on empirical grounds as a resolution of the antinomies of quantum mechanics. The third case study is concerned with systems of relevance logic, which have been the subject of an especially detailed (...)
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  41. Ontology and medical terminology: Why description logics are not enough.Werner Ceusters, Barry Smith & Jim Flanagan - 2003 - In Werner Ceusters, Smith Barry & Jim Flanagan (eds.), in Proceedings of the Conference: Towards an Electronic Patient Record (TEPR 2003). Medical Records Institute.
    Ontology is currently perceived as the solution of first resort for all problems related to biomedical terminology, and the use of description logics is seen as a minimal requirement on adequate ontology-based systems. Contrary to common conceptions, however, description logics alone are not able to prevent incorrect representations; this is because they do not come with a theory indicating what is computed by using them, just as classical arithmetic does not tell us anything about the entities that are (...)
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  42. Conjunction and Disjunction in Infectious Logics.Hitoshi Omori & Damian Szmuc - 2017 - In Alexandru Baltag, Jeremy Seligman & Tomoyuki Yamada (eds.), Logic, Rationality, and Interaction (LORI 2017, Sapporo, Japan). Springer. pp. 268-283.
    In this paper we discuss the extent to which conjunction and disjunction can be rightfully regarded as such, in the context of infectious logics. Infectious logics are peculiar many-valued logics whose underlying algebra has an absorbing or infectious element, which is assigned to a compound formula whenever it is assigned to one of its components. To discuss these matters, we review the philosophical motivations for infectious logics due to Bochvar, Halldén, Fitting, Ferguson and Beall, noticing that (...)
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  43. On Partial and Paraconsistent Logics.Reinhard Muskens - 1999 - Notre Dame Journal of Formal Logic 40 (3):352-374.
    In this paper we consider the theory of predicate logics in which the principle of Bivalence or the principle of Non-Contradiction or both fail. Such logics are partial or paraconsistent or both. We consider sequent calculi for these logics and prove Model Existence. For L4, the most general logic under consideration, we also prove a version of the Craig-Lyndon Interpolation Theorem. The paper shows that many techniques used for classical predicate logic generalise to partial and paraconsistent (...) once the right set-up is chosen. Our logic L4 has a semantics that also underlies Belnap’s [4] and is related to the logic of bilattices. L4 is in focus most of the time, but it is also shown how results obtained for L4 can be transferred to several variants. (shrink)
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  44. Maximality in finite-valued Lukasiewicz logics defined by order filters.Marcelo E. Coniglio, Francesc Esteva, Joan Gispert & Lluis Godo - 2019 - Journal of Logic and Computation 29 (1):125-156.
    In this paper we consider the logics L(i,n) obtained from the (n+1)-valued Lukasiewicz logics L(n+1) by taking the order filter generated by i/n as the set of designated elements. In particular, the conditions of maximality and strong maximality among them are analyzed. We present a very general theorem that provides sufficient conditions for maximality between logics. As a consequence of this theorem, it is shown that L(i,n) is maximal w.r.t. CPL whenever n is prime. Concerning strong maximality (...)
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  45. Semantics for Second Order Relevant Logics.Shay Logan - forthcoming - In Andrew Tedder, Shawn Standefer & Igor Sedlar (eds.), New Directions in Relevant Logic. Springer.
    Here's the thing: when you look at it from just the right angle, it's entirely obvious how semantics for second-order relevant logics ought to go. Or at least, if you've understood how semantics for first-order relevant logics ought to go, there are perspectives like this. What's more is that from any such angle, the metatheory that needs doing can be summed up in one line: everything is just as in the first-order case, but with more indices. Of course, (...)
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  46. Theories of truth based on four-valued infectious logics.Damian Szmuc, Bruno Da Re & Federico Pailos - 2020 - Logic Journal of the IGPL 28 (5):712-746.
    Infectious logics are systems that have a truth-value that is assigned to a compound formula whenever it is assigned to one of its components. This paper studies four-valued infectious logics as the basis of transparent theories of truth. This take is motivated as a way to treat different pathological sentences differently, namely, by allowing some of them to be truth-value gluts and some others to be truth-value gaps and as a way to treat the semantic pathology suffered by (...)
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  47. Hierarchies of modal and temporal logics with reference pointers.Valentin Goranko - 1996 - Journal of Logic, Language and Information 5 (1):1-24.
    We introduce and study hierarchies of extensions of the propositional modal and temporal languages with pairs of new syntactic devices: point of reference-reference pointer which enable semantic references to be made within a formula. We propose three different but equivalent semantics for the extended languages, discuss and compare their expressiveness. The languages with reference pointers are shown to have great expressive power (especially when their frugal syntax is taken into account), perspicuous semantics, and simple deductive systems. For instance, Kamp's and (...)
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  48. Effective finite-valued approximations of general propositional logics.Matthias Baaz & Richard Zach - 2008 - In Arnon Avron & Nachum Dershowitz (eds.), Pillars of Computer Science: Essays Dedicated to Boris (Boaz) Trakhtenbrot on the Occasion of His 85th Birthday. Springer Verlag. pp. 107–129.
    Propositional logics in general, considered as a set of sentences, can be undecidable even if they have “nice” representations, e.g., are given by a calculus. Even decidable propositional logics can be computationally complex (e.g., already intuitionistic logic is PSPACE-complete). On the other hand, finite-valued logics are computationally relatively simple—at worst NP. Moreover, finite-valued semantics are simple, and general methods for theorem proving exist. This raises the question to what extent and under what circumstances propositional logics represented (...)
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  49. Swap structures semantics for Ivlev-like modal logics.Marcelo E. Coniglio & Ana Claudia Golzio - 2019 - Soft Computing 23 (7):2243-2254.
    In 1988, J. Ivlev proposed some (non-normal) modal systems which are semantically characterized by four-valued non-deterministic matrices in the sense of A. Avron and I. Lev. Swap structures are multialgebras (a.k.a. hyperalgebras) of a special kind, which were introduced in 2016 by W. Carnielli and M. Coniglio in order to give a non-deterministic semantical account for several paraconsistent logics known as logics of formal inconsistency, which are not algebraizable by means of the standard techniques. Each swap structure induces (...)
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  50. Automating Agential Reasoning: Proof-Calculi and Syntactic Decidability for STIT Logics.Tim Lyon & Kees van Berkel - 2019 - In M. Baldoni, M. Dastani, B. Liao, Y. Sakurai & R. Zalila Wenkstern (eds.), PRIMA 2019: Principles and Practice of Multi-Agent Systems. Springer. pp. 202-218.
    This work provides proof-search algorithms and automated counter-model extraction for a class of STIT logics. With this, we answer an open problem concerning syntactic decision procedures and cut-free calculi for STIT logics. A new class of cut-free complete labelled sequent calculi G3LdmL^m_n, for multi-agent STIT with at most n-many choices, is introduced. We refine the calculi G3LdmL^m_n through the use of propagation rules and demonstrate the admissibility of their structural rules, resulting in auxiliary calculi Ldm^m_nL. In the single-agent (...)
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