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  1. added 2020-03-29
    Weak Necessity on Weak Kleene Matrices.Fabrice Correia - 2002 - In Marcus Kracht, Maarten de Rijke, Heinrich Wansing & Michael Zakharyaschev (eds.), Advances in Modal Logic. CSLI Publications. pp. 73-90.
    A possible world semantics for standard modal languages is presented, where the valuation functions are allowed to be partial, the truth–functional connectives are interpreted according to weak Kleene matrices, and the necessity operator is given a “weak” interpretation. Completeness and incompleteness results for some (axiomatic) systems are then established. Extensions of these modal logics in which figure “statability” operators are also examined.
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  2. added 2019-12-20
    Negation on the Australian Plan.Francesco Berto & Greg Restall - 2019 - Journal of Philosophical Logic 48 (6):1119-1144.
    We present and defend the Australian Plan semantics for negation. This is a comprehensive account, suitable for a variety of different logics. It is based on two ideas. The first is that negation is an exclusion-expressing device: we utter negations to express incompatibilities. The second is that, because incompatibility is modal, negation is a modal operator as well. It can, then, be modelled as a quantifier over points in frames, restricted by accessibility relations representing compatibilities and incompatibilities between such points. (...)
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  3. added 2019-10-15
    (Meta)Inferential Levels of Entailment Beyond the Tarskian Paradigm.Eduardo Alejandro Barrio, Federico Pailos & Damian Szmuc - forthcoming - Synthese:1-25.
    In this paper we discuss the extent to which the very existence of substructural logics puts the Tarskian conception of logical systems in jeopardy. In order to do this, we highlight the importance of the presence of different levels of entailment in a given logic, looking not only at inferences between collections of formulae but also at inferences between collections of inferences—and more. We discuss appropriate refinements or modifications of the usual Tarskian identity criterion for logical systems, and propose an (...)
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  4. added 2019-08-14
    Iterated Reflection Over Full Disquotational Truth.Fischer Martin, Nicolai Carlo & Horsten Leon - 2017 - Journal of Logic and Computation 27 (8):2631-2651.
    Iterated reflection principles have been employed extensively to unfold epistemic commitments that are incurred by accepting a mathematical theory. Recently this has been applied to theories of truth. The idea is to start with a collection of Tarski-biconditionals and arrive by iterated reflection at strong compositional truth theories. In the context of classical logic, it is incoherent to adopt an initial truth theory in which A and ‘A is truen’ are inter-derivable. In this article, we show how in the context (...)
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  5. added 2019-07-29
    A Formalisation, Using Non-Standard Rules, Of A 5-Valued Propositional Calculus.Alan Rose† - 1987 - Mathematical Logic Quarterly 33 (2):187-192.
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  6. added 2019-07-04
    Peter Geach: A Few Personal Remarks.Arthur Gibson - 2015 - Philosophical Investigations 38 (1-2):25-33.
    Personal biographical outline of being taught by, and encounters with, Peter Geach.
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  7. added 2019-06-06
    Set-Valued Set Theory: Part Two.E. William Chapin - 1975 - Notre Dame Journal of Formal Logic 16:255.
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  8. added 2019-06-06
    Set-Valued Set Theory: Part One.E. William Chapin - 1974 - Notre Dame Journal of Formal Logic 15:619.
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  9. added 2019-06-06
    An Example of a Non-Axiomatizable Many Valued Logic.Andrzej Mostowski - 1961 - Mathematical Logic Quarterly 7 (1-5):72-76.
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  10. added 2019-06-06
    Review: O. B. Lupanov, On the Possibilities of Designing Circuits Out of Various Elements; O. B. Lupanov, On the Synthesis of Contact Circuits; O. B. Lupanov, On the Synthesis of Contact Networks. [REVIEW]Edward F. Moore & O. B. Lupanov - 1959 - Journal of Symbolic Logic 24 (1):76.
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  11. added 2019-06-06
    On the Representation of Finitely Many-Valued Logics by Electric Circuits.Katuzi Ono & Toshihiko Kurihara - 1957 - Journal of Symbolic Logic 22 (1):102.
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  12. added 2019-06-06
    Rose Alan. A Formalisation of the 2-Valued Propositional Calculus with Self-Dual Primitives. Mathematische Annalen, Vol. 127 , Pp. 255–257. [REVIEW]Alonzo Church - 1954 - Journal of Symbolic Logic 19 (4):295-295.
  13. added 2019-06-06
    Rosser Barkley. The Introduction of Quantification Into a Three-Valued Logic. Ditto, 6 Pp.Alonzo Church - 1939 - Journal of Symbolic Logic 4 (4):170-170.
  14. added 2019-06-03
    Curry’s Paradox and Ω -Inconsistency.Andrew Bacon - 2013 - Studia Logica 101 (1):1-9.
    In recent years there has been a revitalised interest in non-classical solutions to the semantic paradoxes. In this paper I show that a number of logics are susceptible to a strengthened version of Curry's paradox. This can be adapted to provide a proof theoretic analysis of the omega-inconsistency in Lukasiewicz's continuum valued logic, allowing us to better evaluate which logics are suitable for a naïve truth theory. On this basis I identify two natural subsystems of Lukasiewicz logic which individually, but (...)
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  15. added 2019-06-03
    Arto Salomaa. Some Analogues of Sheffet Functions in Infinite-Valued Logics. Proceedings of a Colloquium on Modal and Many-Valued Logics, Helsinki, 23–26 August, 1962, Acta Philosophica Fennica, No. 16, Helsinki1963, Pp. 227–235. [REVIEW]Norman M. Martin - 1966 - Journal of Symbolic Logic 31 (1):118-119.
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  16. added 2019-06-03
    Federico M. Sioson. Further Axiomatizations of the Łukasiewicz Three-Valued Calculus. Notre Dame Journal of Formal Logic, Vol. 5 No. 1 , Pp. 62–70.Atwell R. Turquette - 1966 - Journal of Symbolic Logic 31 (3):500.
  17. added 2019-05-13
    Atwell R. Turquette. Independent Axioms for Infinite-Valued Logic. The Journal of Symbolic Logic, Vol. 28 No. 3 , Pp. 217–221.Louise Hay - 1966 - Journal of Symbolic Logic 31 (4):665.
  18. added 2019-04-08
    A Hierarchy of Classical and Paraconsistent Logics.Eduardo Alejandro Barrio, Federico Pailos & Damian Szmuc - 2020 - Journal of Philosophical Logic 49 (1):93-120.
    In this article, we will present a number of technical results concerning Classical Logic, ST and related systems. Our main contribution consists in offering a novel identity criterion for logics in general and, therefore, for Classical Logic. In particular, we will firstly generalize the ST phenomenon, thereby obtaining a recursively defined hierarchy of strict-tolerant systems. Secondly, we will prove that the logics in this hierarchy are progressively more classical, although not entirely classical. We will claim that a logic is to (...)
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  19. added 2019-03-24
    The Lvov-Warsaw School. Past and Present.Urszula Wybraniec-Skardowska & Ángel Garrido (eds.) - 2018 - Cham, Switzerland: Springer- Birkhauser,.
    This is a collection of new investigations and discoveries on the history of a great tradition, the Lvov-Warsaw School of logic , philosophy and mathematics, by the best specialists from all over the world. The papers range from historical considerations to new philosophical, logical and mathematical developments of this impressive School, including applications to Computer Science, Mathematics, Metalogic, Scientific and Analytic Philosophy, Theory of Models and Linguistics.
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  20. added 2019-03-11
    Skolem Functions in Non-Classical Logics.Tore Fjetland Øgaard - 2017 - Australasian Journal of Logic 14 (1):181-225.
    This paper shows how to conservatively extend theories formulated in non-classical logics such as the Logic of Paradox, the Strong Kleene Logic and relevant logics with Skolem functions. Translations to and from the language extended by Skolem functions into the original one are presented and shown to preserve derivability. It is also shown that one may not always substitute s=f(t) and A(t, s) even though A determines the extension of a function and f is a Skolem function for A.
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  21. added 2019-03-09
    Une sémantique générale des croyances justifiées.Fabien Schang & Alexandre Costa Leite - 2016 - CLE-Prints 16 (3):1-24.
    Nous proposons une logique épistémique quadrivalente AR4.
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  22. added 2019-03-09
    A Plea for Epistemic Truth: Jaina Logic From a Many-Valued Perspective.Fabien Schang - 2009 - In A. Schuman (ed.), Logic in Religious Discourse. Ontos Verlag. pp. 54--83.
    We present the Jaina theory of sevenfold predication as a 7-valued logic, in which every logical value consists in a 3-tuple of opinions. A question-answer semantics is used in order to give an intuitive characterization of these logical values in terms of opinion polls. Two different interpretations are plausible for the latest sort of opinion, depending upon whether "non-assertability" refers to incompleteness or inconsistency. It is shown hat the incomplete version of JL_{G} is equivalent to Kleene's logic K3, whereas the (...)
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  23. added 2019-02-15
    Syntactic Characterizations of First-Order Structures in Mathematical Fuzzy Logic.Guillermo Badia, Pilar Dellunde, Vicent Costa & Carles Noguera - forthcoming - Soft Computing.
    This paper is a contribution to graded model theory, in the context of mathematical fuzzy logic. We study characterizations of classes of graded structures in terms of the syntactic form of their first-order axiomatization. We focus on classes given by universal and universal-existential sentences. In particular, we prove two amalgamation results using the technique of diagrams in the setting of structures valued on a finite MTL-algebra, from which analogues of the Łoś–Tarski and the Chang–Łoś–Suszko preservation theorems follow.
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  24. added 2019-02-07
    Relevant Logics Obeying Component Homogeneity.Roberto Ciuni, Damian Szmuc & Thomas Macaulay Ferguson - 2018 - Australasian Journal of Logic 15 (2):301-361.
    This paper discusses three relevant logics that obey Component Homogeneity - a principle that Goddard and Routley introduce in their project of a logic of significance. The paper establishes two main results. First, it establishes a general characterization result for two families of logic that obey Component Homogeneity - that is, we provide a set of necessary and sufficient conditions for their consequence relations. From this, we derive characterization results for S*fde, dS*fde, crossS*fde. Second, the paper establishes complete sequent calculi (...)
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  25. added 2019-02-07
    A Note on Goddard and Routley's Significance Logic.Damian Szmuc & Hitoshi Omori - 2018 - Australasian Journal of Logic 15 (2):431-448.
    The present note revisits the joint work of Leonard Goddard and Richard Routley on significance logics with the aim of shedding new light on their understanding by studying them under the lens of recent semantic developments, such as the plurivalent semantics developed by Graham Priest. These semantics allow sentences to receive one, more than one, or no truth-value at all from a given carrier set. Since nonsignificant sentences are taken to be neither true nor false, i.e. truth-value gaps, in this (...)
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  26. added 2019-02-04
    Recapture, Transparency, Negation and a Logic for the Catuskoti.Adrian Kreutz - 2019 - Comparative Philosophy 10 (1):67-92.
    The recent literature on Nāgārjuna’s catuṣkoṭi centres around Jay Garfield’s (2009) and Graham Priest’s (2010) interpretation. It is an open discussion to what extent their interpretation is an adequate model of the logic for the catuskoti, and the Mūla-madhyamaka-kārikā. Priest and Garfield try to make sense of the contradictions within the catuskoti by appeal to a series of lattices – orderings of truth-values, supposed to model the path to enlightenment. They use Anderson & Belnaps's (1975) framework of First Degree Entailment. (...)
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  27. added 2019-01-09
    On Graph-Theoretic Fibring of Logics.A. Sernadas, C. Sernadas, J. Rasga & M. Coniglio - 2009 - Journal of Logic and Computation 19 (6):1321-1357.
    A graph-theoretic account of fibring of logics is developed, capitalizing on the interleaving characteristics of fibring at the linguistic, semantic and proof levels. Fibring of two signatures is seen as a multi-graph (m-graph) where the nodes and the m-edges include the sorts and the constructors of the signatures at hand. Fibring of two models is a multi-graph (m-graph) where the nodes and the m-edges are the values and the operations in the models, respectively. Fibring of two deductive systems is an (...)
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  28. added 2019-01-09
    A Graph-Theoretic Account of Logics.A. Sernadas, C. Sernadas, J. Rasga & Marcelo E. Coniglio - 2009 - Journal of Logic and Computation 19 (6):1281-1320.
    A graph-theoretic account of logics is explored based on the general notion of m-graph (that is, a graph where each edge can have a finite sequence of nodes as source). Signatures, interpretation structures and deduction systems are seen as m-graphs. After defining a category freely generated by a m-graph, formulas and expressions in general can be seen as morphisms. Moreover, derivations involving rule instantiation are also morphisms. Soundness and completeness theorems are proved. As a consequence of the generality of the (...)
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  29. added 2018-11-29
    Defining LFIs and LFUs in Extensions of Infectious Logics.Szmuc Damian Enrique - 2016 - Journal of Applied Non-Classical Logics 26 (4):286-314.
    The aim of this paper is to explore the peculiar case of infectious logics, a group of systems obtained generalizing the semantic behavior characteristic of the -fragment of the logics of nonsense, such as the ones due to Bochvar and Halldén, among others. Here, we extend these logics with classical negations, and we furthermore show that some of these extended systems can be properly regarded as logics of formal inconsistency and logics of formal undeterminedness.
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  30. added 2018-10-18
    A Temporal Semantics for Basic Logic.Stefano Aguzzoli, Matteo Bianchi & Vincenzo Marra - 2009 - Studia Logica 92 (2):147-162.
    In the context of truth-functional propositional many-valued logics, Hájek’s Basic Fuzzy Logic BL [14] plays a major rôle. The completeness theorem proved in [7] shows that BL is the logic of all continuous t -norms and their residua. This result, however, does not directly yield any meaningful interpretation of the truth values in BL per se . In an attempt to address this issue, in this paper we introduce a complete temporal semantics for BL. Specifically, we show that BL formulas (...)
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  31. added 2018-10-03
    Track-Down Operations on Bilattices.Damian Szmuc - 2018 - In Robert Wille & Martin Lukac (eds.), Proceedings of the 48th IEEE International Symposium on Multiple-Valued Logic. Los Alamitos, California, EE. UU.: pp. 74-79.
    This paper discusses a dualization of Fitting's notion of a "cut-down" operation on a bilattice, rendering a "track-down" operation, later used to represent the idea that a consistent opinion cannot arise from a set including an inconsistent opinion. The logic of track-down operations on bilattices is proved equivalent to the logic d_Sfde, dual to Deutsch's system S_fde. Furthermore, track-down operations are employed to provide an epistemic interpretation for paraconsistent weak Kleene logic. Finally, two logics of sequential combinations of cut-and track-down (...)
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  32. added 2018-09-06
    Partial Information.Reinhard Muskens - 1993 - In R. E. Asher & J. M. Y. Simpson (eds.), The Encyclopedia of Language and Linguistics. Pergamon Press. pp. 6--2952.
    the world of phenomena is immensely large this means we can perceive only part of the world. We see, feel and hear parts of reality, not the whole of it, and it seems that a sentence containing a verb of perception like 'John sees a house burn' is most naturally treated as saying that the subject sees an incomplete world in which the embedded sentence is true (see Barwise (1981) for this analysis). But if we want to analyse perception verbs (...)
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  33. added 2018-09-04
    Truth and Generalized Quantification.Bruno Whittle - 2019 - Australasian Journal of Philosophy 97 (2):340-353.
    Kripke [1975] gives a formal theory of truth based on Kleene's strong evaluation scheme. It is probably the most important and influential that has yet been given—at least since Tarski. However, it has been argued that this theory has a problem with generalized quantifiers such as All—that is, All ϕs are ψ—or Most. Specifically, it has been argued that such quantifiers preclude the existence of just the sort of language that Kripke aims to deliver—one that contains its own truth predicate. (...)
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  34. added 2018-08-27
    A Calculus for Belnap's Logic in Which Each Proof Consists of Two Trees.Stefan Wintein & Reinhard Muskens - 2012 - Logique Et Analyse 220:643-656.
    In this paper we introduce a Gentzen calculus for (a functionally complete variant of) Belnap's logic in which establishing the provability of a sequent in general requires \emph{two} proof trees, one establishing that whenever all premises are true some conclusion is true and one that guarantees the falsity of at least one premise if all conclusions are false. The calculus can also be put to use in proving that one statement \emph{necessarily approximates} another, where necessary approximation is a natural dual (...)
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  35. added 2018-08-26
    Interpolation in 16-Valued Trilattice Logics.Reinhard Muskens & Stefan Wintein - 2018 - Studia Logica 106 (2):345-370.
    In a recent paper we have defined an analytic tableau calculus PL_16 for a functionally complete extension of Shramko and Wansing's logic based on the trilattice SIXTEEN_3. This calculus makes it possible to define syntactic entailment relations that capture central semantic relations of the logic---such as the relations |=_t, |=_f, and |=_i that each correspond to a lattice order in SIXTEEN_3; and |=, the intersection of |=_t and |=_f,. -/- It turns out that our method of characterising these semantic relations---as (...)
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  36. added 2018-08-26
    16TaP: A Toy Tableau Theorem Prover for 16-Valued Trilattice Logics.Reinhard Muskens - 2017 - A Programming Road to Logic, Maths, Language, and Philosophy : A Tribute to Jan van Eijck on the Occasion of His Retirement.
    A short description of a toy theorem prover for 16-valued trilattice logics. Written for the occasion of my friend's Jan van Eijck's retirement. With a link to a swish interface to the prolog prover.
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  37. added 2018-06-07
    Sistema Experto en Deducción dentro de la Lógica Normal Trivalente.Gabriel Garduño-Soto, David René Thierry García, Rafael Vidal Uribe & Hugo Padilla Chacón - 1990 - In VIa. Conferencia Internacional: Las Computadoras en Instituciones de Educación y de Investigación. Cómputo Académico, UNAM, UNISYS, México, octubre 3–5, 1990. Mexico City: National Autonomous University of Mexico.
    Proceeding of the work in trivalent logic developped under the direction of the professor Hugo Padilla Chacón at the 90's at the National Autonome University of México. Program in RLisp.
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  38. added 2018-05-12
    Proof Theory of Finite-Valued Logics.Richard Zach - 1993 - Dissertation, Technische Universität Wien
    The proof theory of many-valued systems has not been investigated to an extent comparable to the work done on axiomatizatbility of many-valued logics. Proof theory requires appropriate formalisms, such as sequent calculus, natural deduction, and tableaux for classical (and intuitionistic) logic. One particular method for systematically obtaining calculi for all finite-valued logics was invented independently by several researchers, with slight variations in design and presentation. The main aim of this report is to develop the proof theory of finite-valued first order (...)
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  39. added 2018-04-13
    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). Berlin: 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 none of them discusses (...)
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  40. added 2018-04-07
    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.
  41. added 2018-03-22
    Weak Necessity on Weak Kleene Matrices.Fabrice Correia - 2002 - In Frank Wolter, Heinrich Wansing, Maarten de Rijke & Michael Zakharyaschev (eds.), Advances in Modal Logic, Volume 3. CSLI Publications. pp. 73-90.
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  42. added 2018-02-21
    New Dimensions of the Square of Opposition.Jean-Yves Beziau & Stamatios Gerogiorgakis (eds.) - 2017 - Munich: Philosophia.
    The square of opposition is a diagram related to a theory of oppositions that goes back to Aristotle. Both the diagram and the theory have been discussed throughout the history of logic. Initially, the diagram was employed to present the Aristotelian theory of quantification, but extensions and criticisms of this theory have resulted in various other diagrams. The strength of the theory is that it is at the same time fairly simple and quite rich. The theory of oppositions has recently (...)
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  43. added 2018-02-17
    New Waves in Truth.Cory Wright & Nikolaj Jang Lee Linding Pedersen (eds.) - 2010 - Palgrave-Macmillan.
    What is truth? Philosophers are interested in a range of issues involving the concept of truth beginning with what sorts of things can be true. This is a collection of eighteen new and original research papers on truth and other alethic phenomena by twenty of the most promising young scholars working on truth today.
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  44. added 2018-02-01
    Logically Impossible Worlds.Koji Tanaka - 2018 - Australasian Journal of Logic 15 (2):489.
    What does it mean for the laws of logic to fail? My task in this paper is to answer this question. I use the resources that Routley/Sylvan developed with his collaborators for the semantics of relevant logics to explain a world where the laws of logic fail. I claim that the non-normal worlds that Routley/Sylvan introduced are exactly such worlds. To disambiguate different kinds of impossible worlds, I call such worlds logically impossible worlds. At a logically impossible world, the laws (...)
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  45. added 2017-10-13
    Belief Dynamics: (Epistemo)Logical Investigations.Allard Tamminga - 2001 - Dissertation, University of Amsterdam
    C.S. Peirce's and Isaac Levi's accounts of the belief-doubt-belief model are discussed and evaluated. It is argued that the contemporary study of belief change has metamorphosed into a branch of philosophical logic where empirical considerations have become obsolete. A case is made for reformulations of belief change systems that do allow for empirical tests. Last, a belief change system is presented that (1) uses finite representations of information, (2) can adequately deal with inconsistencies, (3) has finite operations of change, (4) (...)
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  46. added 2017-10-10
    Effective Finite-Valued Approximations of General Propositional Logics.Matthias Baaz & Richard Zach - 2008 - In Arnon Avron, Nachum Dershowitz & Alexander Rabinovich (eds.), Pillars of Computer Science: Essays Dedicated to Boris (Boaz) Trakhtenbrot on the Occasion of His 85th Birthday. Berlin: Springer. 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 in various ways can (...)
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  47. added 2017-10-10
    Completeness of a Hypersequent Calculus for Some First-Order Gödel Logics with Delta.Matthias Baaz, Norbert Preining & Richard Zach - 2006 - In 36th International Symposium on Multiple-valued Logic. May 2006, Singapore. Proceedings. Los Alamitos: IEEE Press.
    All first-order Gödel logics G_V with globalization operator based on truth value sets V C [0,1] where 0 and 1 lie in the perfect kernel of V are axiomatized by Ciabattoni’s hypersequent calculus HGIF.
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  48. added 2017-10-10
    Hypersequents and the Proof Theory of Intuitionistic Fuzzy Logic.Matthias Baaz & Richard Zach - 2000 - In Peter G. Clote & Helmut Schwichtenberg (eds.), Computer Science Logic. 14th International Workshop, CSL 2000. Berlin: Springer. pp. 187– 201.
    Takeuti and Titani have introduced and investigated a logic they called intuitionistic fuzzy logic. This logic is characterized as the first-order Gödel logic based on the truth value set [0,1]. The logic is known to be axiomatizable, but no deduction system amenable to proof-theoretic, and hence, computational treatment, has been known. Such a system is presented here, based on previous work on hypersequent calculi for propositional Gödel logics by Avron. It is shown that the system is sound and complete, and (...)
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  49. added 2017-10-10
    Approximating Propositional Calculi by Finite-Valued Logics.Matthias Baaz & Richard Zach - 1994 - In 24th International Symposium on Multiple-valued Logic, 1994. Proceedings. Los Alamitos: IEEE Press. pp. 257–263.
    The problem of approximating a propositional calculus is to find many-valued logics which are sound for the calculus (i.e., all theorems of the calculus are tautologies) with as few tautologies as possible. This has potential applications for representing (computationally complex) logics used in AI by (computationally easy) many-valued logics. It is investigated how far this method can be carried using (1) one or (2) an infinite sequence of many-valued logics. It is shown that the optimal candidate matrices for (1) can (...)
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  50. added 2017-10-10
    Elimination of Cuts in First-Order Finite-Valued Logics.Matthias Baaz, Christian G. Fermüller & Richard Zach - 1994 - Journal of Information Processing and Cybernetics EIK 29 (6):333-355.
    A uniform construction for sequent calculi for finite-valued first-order logics with distribution quantifiers is exhibited. Completeness, cut-elimination and midsequent theorems are established. As an application, an analog of Herbrand’s theorem for the four-valued knowledge-representation logic of Belnap and Ginsberg is presented. It is indicated how this theorem can be used for reasoning about knowledge bases with incomplete and inconsistent information.
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