Search results for 'Free Logic' (try it on Scholar)

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  1. G. Aldo Antonelli (2000). Proto-Semantics for Positive Free Logic. Journal of Philosophical Logic 29 (3):277-294.score: 186.0
    This paper presents a bivalent extensional semantics for positive free logic without resorting to the philosophically questionable device of using models endowed with a separate domain of "non-existing" objects. The models here introduced have only one (possibly empty) domain, and a partial reference function for the singular terms (that might be undefined at some arguments). Such an approach provides a solution to an open problem put forward by Lambert, and can be viewed as supplying a version of parametrized (...)
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  2. Dolf Rami, Non‐Standard Neutral Free Logic, Empty Names and Negative Existentials.score: 180.0
    In this paper I am concerned with an analysis of negative existential sentences that contain proper names only by using negative or neutral free logic. I will compare different versions of neutral free logic with the standard system of negative free logic (Burge, Sainsbury) and aim to defend my version of neutral free logic that I have labeled non-standard neutral free logic.
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  3. Dolf Rami, Existence and Free Logic.score: 180.0
    In this paper I aim to defend a first‐order non‐discriminating property view concerning existence. The version of this view that I prefer is based on negative (or a specific neutral) free logic that treats the existence predicate as first‐order logical predicate. I will provide reasons why such a view is more plausible than a second‐order discriminating property view concerning existence and I will also discuss four challenges for the proposed view and provide solutions to them.
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  4. Karel Lambert (2003). Free Logic: Selected Essays. New Yorkcambridge University Press.score: 180.0
    Free logic is an important field of philosophical logic that first appeared in the 1950s. J. Karel Lambert was one of its founders and coined the term itself. The essays in this collection (written over a period of 40 years) explore the philosophical foundations of free logic and its application to areas as diverse as the philosophy of religion and computer science. Amongst the applications on offer are those to the analysis of existence statements, to (...)
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  5. Norbert Gratzl (2010). A Sequent Calculus for a Negative Free Logic. Studia Logica 96 (3):331-348.score: 180.0
    This article presents a sequent calculus for a negative free logic with identity, called N . The main theorem (in part 1) is the admissibility of the Cut-rule. The second part of this essay is devoted to proofs of soundness, compactness and completeness of N relative to a standard semantics for negative free logic.
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  6. Maria Lasonen-Aarnio (2008). Why the Externalist is Better Off Without Free Logic: A Reply to McKinsey. Dialectica 62 (4):535-540.score: 180.0
    McKinsey-style incompatibilist arguments attempt to show that the thesis that subjects have privileged, a priori access to the contents of their thoughts is incompatible with semantic externalism. This incompatibility follows – it is urged – from the fact that these theses jointly entail an absurd conclusion, namely, the possibility of a priori knowledge of the world. In a recent paper I argued that a large and important class of such arguments exemplifies a dialectical failure: if they are valid, the putatively (...)
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  7. Ermanno Bencivenga (forthcoming). Jaśkowski's Universally Free Logic. Studia Logica:1-8.score: 180.0
    A universally free logic is a system of quantification theory, with or without identity, whose theses remain logically true if (a) the domain of quantification is empty and (b) some of the singular terms present in the language do not denote existing objects. In the West, (inclusive) logics satisfying (a) and (free) ones satisfying (b) were developed starting in the 1950s. But Stanisław Jaśkowski preceded all this work by some twenty years: his paper “On the Rules of (...)
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  8. Karel Lambert (ed.) (1991). Philosophical Applications of Free Logic. Oxford University Press.score: 180.0
    Free logic, an alternative to traditional logic, has been seen as a useful avenue of approach to a number of philosophical issues of contemporary interest. In this collection, Karel Lambert, one of the pioneers in, and the most prominent exponent of, free logic, brings together a variety of published essays bearing on the application of free logic to philosophical topics ranging from set theory and logic to metaphysics and the philosophy of religion. (...)
     
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  9. Arief Daynes (2006). A New Technique for Proving Realisability and Consistency Theorems Using Finite Paraconsistent Models of Cut‐Free Logic. Mathematical Logic Quarterly 52 (6):540-554.score: 156.0
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  10. Brian Hill & Francesca Poggiolesi (2010). A Contraction-Free and Cut-Free Sequent Calculus for Propositional Dynamic Logic. Studia Logica 94 (1):47 - 72.score: 144.0
    In this paper we present a sequent calculus for propositional dynamic logic built using an enriched version of the tree-hypersequent method and including an infinitary rule for the iteration operator. We prove that this sequent calculus is theoremwise equivalent to the corresponding Hilbert-style system, and that it is contraction-free and cut-free. All results are proved in a purely syntactic way.
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  11. Cristina Coppola, Giangiacomo Gerla & Annamaria Miranda (2010). Point-Free Foundation of Geometry and Multivalued Logic. Notre Dame Journal of Formal Logic 51 (3):383-405.score: 138.0
    Whitehead, in two basic books, considers two different approaches to point-free geometry: the inclusion-based approach , whose primitive notions are regions and inclusion relation between regions, and the connection-based approach , where the connection relation is considered instead of the inclusion. We show that the latter cannot be reduced to the first one, although this can be done in the framework of multivalued logics.
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  12. Francesco Orilia (1994). Belief Representation in a Deductivist Type-Free Doxastic Logic. Minds and Machines 4 (2):163-203.score: 132.0
    Konolige''s technical notion of belief based on deduction structures is briefly reviewed and its usefulness for the design of artificial agents with limited representational and deductive capacities is pointed out. The design of artificial agents with more sophisticated representational and deductive capacities is then taken into account. Extended representational capacities require in the first place a solution to the intensional context problems. As an alternative to Konolige''s modal first-order language, an approach based on type-free property theory is proposed. It (...)
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  13. Mark Sainsbury (2005). Names in Free Logical Truth Theory. In José Luis Bermúdez (ed.), Thought, Reference, and Experience: Themes From the Philosophy of Gareth Evans. Clarendon Press.score: 128.0
    Evans envisaged a language containing both Russellian and descriptive names. A language with descriptive names, which can contribute to truth conditions even if they have no bearer, needs a free logical truth theory. But a metalanguage with this logic threatens to emasculate Russellian names. The paper details this problem and shows, on Evans's behalf, how it might be resolved.
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  14. Newton C. A. da Costa & Otavio Bueno (1999). Quasi-Truth, Supervaluations and Free Logic. History and Philosophy of Logic 20 (3-4):215-226.score: 126.0
    The partial structures approach has two major components: a broad notion of structure (partial structure) and a weak notion of truth (quasi-truth). In this paper, we discuss the relationship between this approach and free logic. We also compare the model-theoretic analysis supplied by partial structures with the method of supervaluations, which was initially introduced as a technique to provide a semantic analysis of free logic. We then combine the three formal frameworks (partial structures, free (...) and supervaluations), and apply the resulting approach to accommodate semantic paradoxes. (shrink)
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  15. Hans-Peter Leeb (2006). State-of-Affairs Semantics for Positive Free Logic. Journal of Philosophical Logic 35 (2):183 - 208.score: 126.0
    In the following the details of a state-of-affairs semantics for positive free logic are worked out, based on the models of common inner domain - outer domain semantics. Lambert's PFL system is proven to be weakly adequate (i.e., sound and complete) with respect to that semantics by demonstrating that the concept of logical truth definable therein coincides with that one of common truth-value semantics for PFL. Furthermore, this state-of-affairs semantics resists the challenges stemming from the slingshot argument since (...)
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  16. Karel Lambert (1981). On the Philosophical Foundations of Free Logic. Inquiry 24 (2):147 – 203.score: 120.0
    The essay outlines the character of free logic, and motivation for its construction and development. It details some technical achievements of high philosophical interest, but urges that the role of existence assumptions in logic is still not fully understood, that unresolved old problems, both technical and philosophical, abound, and presents some new problems of considerable philosophical import in free logic.
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  17. R. M. Sainsbury (2006). Facts and Free Logic. Protosociology 26:119–27.score: 120.0
    Comment on S. Neale's, "Facts and Free Logic".
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  18. Peter Milne (2007). Existence and Identity in Free Logic: Two Comments. Mind 116 (464):1079-1082.score: 120.0
    Professor Tennant and I agree on much regarding the proof-theoretic semantics of free logic. Here I point to two issues, one on which we disagree, the other on which I find it hard to say how closely we may agree. The first concerns the exact content of Tennant's Rule of Atomic Denotation. The second concerns the nature of assumptions whose formal counterparts contain parametric occurrences of names.
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  19. Neil Tennant (2007). Existence and Identity in Free Logic: A Problem for Inferentialism? Mind 116 (464):1055-1078.score: 120.0
    Peter Milne (2007) poses two challenges to the inferential theorist of meaning. This study responds to both. First, it argues that the method of natural deduction idealizes the essential details of correct informal deductive reasoning. Secondly, it explains how rules of inference in free logic can determine unique senses for the existential quantifier and the identity predicate. The final part of the investigation brings out an underlying order in a basic family of free logics.
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  20. Peter van Inwagen (1990). Logic and the Free Will Problem. Social Theory and Practice 16 (3):277-90.score: 120.0
  21. Wayne Aitken & Jeffrey A. Barrett (2007). Stability and Paradox in Algorithmic Logic. Journal of Philosophical Logic 36 (1):61 - 95.score: 114.0
    There is significant interest in type-free systems that allow flexible self-application. Such systems are of interest in property theory, natural language semantics, the theory of truth, theoretical computer science, the theory of classes, and category theory. While there are a variety of proposed type-free systems, there is a particularly natural type-free system that we believe is prototypical: the logic of recursive algorithms. Algorithmic logic is the study of basic statements concerning algorithms and the algorithmic rules (...)
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  22. Dorota Leszczyńska-Jasion (2009). A Loop-Free Decision Procedure for Modal Propositional Logics K4, S4 and S. Journal of Philosophical Logic 38 (2):151 - 177.score: 114.0
    The aim of this paper is to present a loop-free decision procedure for modal propositional logics K4, S4 and S5. We prove that the procedure terminates and that it is sound and complete. The procedure is based on the method of Socratic proofs for modal logics, which is grounded in the logic of questions IEL.
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  23. Jeffrey Barrett (2007). Stability and Paradox in Algorithmic Logic. Journal of Philosophical Logic 36 (1):61 - 95.score: 114.0
    There is significant interest in type-free systems that allow flexible self-application. Such systems are of interest in property theory, natural language semantics, the theory of truth, theoretical computer science, the theory of classes, and category theory. While there are a variety of proposed type-free systems, there is a particularly natural type-free system that we believe is prototypical: the logic of recursive algorithms. Algorithmic logic is the study of basic statements concerning algorithms and the algorithmic rules (...)
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  24. Kenneth A. Bowen (1980). Interpolation in Loop-Free Logic. Studia Logica 39 (2-3):297 - 310.score: 114.0
    Model-theoretic methods are used to extend Craig's Interpolation Theorem to the loop-free portion of Pratt's dynamic logic of programs with simple assignments.
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  25. Andrew Bacon (2013). Quantificational Logic and Empty Names. Philosophers' Imprint 13 (24).score: 108.0
    The result of combining classical quantificational logic with modal logic proves necessitism – the claim that necessarily everything is necessarily identical to something. This problem is reflected in the purely quantificational theory by theorems such as $\exists xt = x$; it is a theorem, for example, that something is identical to Timothy Williamson. The standard way to avoid these consequences is to weaken the theory of quantification to a certain kind of free logic. However, it has (...)
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  26. Carl J. Posy (1982). A Free IPC is a Natural Logic: Strong Completeness for Some Intuitionistic Free Logics. Topoi 1 (1-2):30-43.score: 108.0
    IPC, the intuitionistic predicate calculus, has the property(i) Vc(A c /x) xA.Furthermore, for certain important , IPC has the converse property (ii) xA Vc(A c /x). (i) may be given up in various ways, corresponding to different philosophic intuitions and yielding different systems of intuitionistic free logic. The present paper proves the strong completeness of several of these with respect to Kripke style semantics. It also shows that giving up (i) need not force us to abandon the analogue (...)
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  27. Roy Dyckhoff & Luis Pinto (1998). Cut-Elimination and a Permutation-Free Sequent Calculus for Intuitionistic Logic. Studia Logica 60 (1):107-118.score: 108.0
    We describe a sequent calculus, based on work of Herbelin, of which the cut-free derivations are in 1-1 correspondence with the normal natural deduction proofs of intuitionistic logic. We present a simple proof of Herbelin's strong cut-elimination theorem for the calculus, using the recursive path ordering theorem of Dershowitz.
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  28. Jarmo Kontinen (2013). Coherence and Computational Complexity of Quantifier-Free Dependence Logic Formulas. Studia Logica 101 (2):267-291.score: 108.0
    We study the computational complexity of the model checking problem for quantifier-free dependence logic ${(\mathcal{D})}$ formulas. We characterize three thresholds in the complexity: logarithmic space (LOGSPACE), non-deterministic logarithmic space (NL) and non-deterministic polynomial time (NP).
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  29. Corine Besson (2009). Externalism, Internalism, and Logical Truth. Review of Symbolic Logic 2 (1):1-29.score: 102.0
    The aim of this paper is to show what sorts of logics are required by externalist and internalist accounts of the meanings of natural kind nouns. These logics give us a new perspective from which to evaluate the respective positions in the externalist-internalist debate about the meanings of such nouns. The two main claims of the paper are the following: first, that adequate logics for internalism and externalism about natural kind nouns are second-order logics; second, that an internalist second-order (...) is a free logic—a second order logic free of existential commitments for natural kind nouns, while an externalist second-order logic is not free of existential commitments for natural kind nouns—it is existentially committed. (shrink)
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  30. Francesca Poggiolesi (2009). A Purely Syntactic and Cut-Free Sequent Calculus for the Modal Logic of Provability. Review of Symbolic Logic 2 (4):593-611.score: 102.0
    In this paper we present a sequent calculus for the modal propositional logic GL (the logic of provability) obtained by means of the tree-hypersequent method, a method in which the metalinguistic strength of hypersequents is improved, so that we can simulate trees shapes. We prove that this sequent calculus is sound and complete with respect to the Hilbert-style system GL, that it is contraction free and cut free and that its logical and modal rules are invertible. (...)
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  31. Francesca Poggiolesi (2008). A Cut-Free Simple Sequent Calculus for Modal Logic S. Review of Symbolic Logic 1 (1):3-15.score: 102.0
    In this paper, we present a simple sequent calculus for the modal propositional logic S5. We prove that this sequent calculus is theoremwise equivalent to the Hilbert-style system S5, that it is contraction-free and cut-free, and finally that it is decidable. All results are proved in a purely syntactic way.
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  32. Roy Dyckhoff & Sara Negri (2000). Admissibility of Structural Rules for Contraction-Free Systems of Intuitionistic Logic. Journal of Symbolic Logic 65 (4):1499-1518.score: 102.0
    We give a direct proof of admissibility of cut and contraction for the contraction-free sequent calculus G4ip for intuitionistic propositional logic and for a corresponding multi-succedent calculus: this proof extends easily in the presence of quantifiers, in contrast to other, indirect, proofs. i.e., those which use induction on sequent weight or appeal to admissibility of rules in other calculi.
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  33. Christopher Menzel (1986). A Complete, Type-Free "Second-Order" Logic and Its Philosophical Foundations. CSLI Publications.score: 102.0
    In this report I motivate and develop a type-free logic with predicate quantifiers within the general ontological framework of (nonextensional) properties, relations, and propositions. In Part I, I present the major ideas of the system informally and discuss its philosophical significance, especially with regard to Russell's paradox. In Part II, I prove the soundness, consistency, and completeness of the logic.
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  34. Andreja Prijatelj (1996). Free Algebras Corresponding to Multiplicative Classical Linear Logic and Some of Its Extensions. Notre Dame Journal of Formal Logic 37 (1):53-70.score: 102.0
    In this paper, constructions of free algebras corresponding to multiplicative classical linear logic, its affine variant, and their extensions with -contraction () are given. As an application, the cardinality problem of some one-variable linear fragments with -contraction is solved.
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  35. Theodore Hailperin (1992). Herbrand Semantics, the Potential Infinite, and Ontology-Free Logic. History and Philosophy of Logic 13 (1):69-90.score: 102.0
    This paper investigates the ontological presuppositions of quantifier logic. It is seen that the actual infinite, although present in the usual completeness proofs, is not needed for a proper semantic foundation. Additionally, quantifier logic can be given an adequate formulation in which neither the notion of individual nor that of a predicate appears.
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  36. Siu-Fan Lee (2009). Fregean Free Logics. Philosophical Researches (Dec):123-129.score: 100.0
    This paper asks which free logic a Fregean should adopt. It examines options within the tradition including Carnap’s (1956) chosen object theory, Lehmann’s (1994, 2002) strict Fregean free logic, Woodruff’s (1970) strong table about Boolean operators and Bencivenga’s (1986, 1991) supervaluational semantics. It argues for a neutral free logic in view of its proximity towards explaining natural languages. However, disagreeing with Lehmann, it claims a Fregean should adopt the strong table based on Frege’s discussion (...)
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  37. Ermanno Bencivenga (1976). Set Theory and Free Logic. Journal of Philosophical Logic 5 (1):1 - 15.score: 96.0
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  38. Karel Lambert (1967). Free Logic and the Concept of Existence. Notre Dame Journal of Formal Logic 8 (1-2):133-144.score: 96.0
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  39. Robert K. Meyer & Karel Lambert (1968). Universally Free Logic and Standard Quantification Theory. Journal of Symbolic Logic 33 (1):8-26.score: 96.0
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  40. Scott Lehmann (1994). Strict Fregean Free Logic. Journal of Philosophical Logic 23 (3):307--336.score: 96.0
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  41. Karel Lambert & Ermanno Bencivenga (1986). A Free Logic with Simple and Complex Predicates. Notre Dame Journal of Formal Logic 27 (2):247-256.score: 96.0
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  42. Richard L. Mendelsohn (1989). Objects and Existence: Reflections on Free Logic. Notre Dame Journal of Formal Logic 30 (4):604-623.score: 96.0
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  43. Branislav R. Boričić (1986). A Cut-Free Gentzen-Type System for the Logic of the Weak Law of Excluded Middle. Studia Logica 45 (1):39 - 53.score: 96.0
    The logic of the weak law of excluded middleKC p is obtained by adding the formula A A as an axiom scheme to Heyting's intuitionistic logicH p . A cut-free sequent calculus for this logic is given. As the consequences of the cut-elimination theorem, we get the decidability of the propositional part of this calculus, its separability, equality of the negationless fragments ofKC p andH p , interpolation theorems and so on. From the proof-theoretical point of view, (...)
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  44. Ermanno Bencivenga (1978). A Semantics for a Weak Free Logic. Notre Dame Journal of Formal Logic 19 (4):646-652.score: 96.0
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  45. Peter W. Woodruff (1984). On Supervaluations in Free Logic. Journal of Symbolic Logic 49 (3):943-950.score: 96.0
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  46. Rajeev Gore, Cut-Free Single-Pass Tableaux for the Logic of Common Knowledge.score: 96.0
    We present a cut-free tableau calculus with histories and variables for the EXPTIME-complete multi-modal logic of common knowledge (LCK). Our calculus constructs the tableau using only one pass, so proof-search for testing theoremhood of ϕ does not exhibit the worst-case EXPTIME-behaviour for all ϕ as in two-pass methods. Our calculus also does not contain a “finitized ω-rule” so that it detects cyclic branches as soon as they arise rather than by worst-case exponential branching with respect to the size (...)
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  47. Ermanno Bencivenga (1980). A Weak Free Logic with the Existence Sign. Notre Dame Journal of Formal Logic 21 (3):572-576.score: 96.0
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  48. Linda Postniece, Combining Derivations and Refutations for Cut-Free Completeness in Bi-Intuitionistic Logic.score: 96.0
    Bi-intuitionistic logic is the union of intuitionistic and dual intuitionistic logic, and was introduced by Rauszer as a Hilbert calculus with algebraic and Kripke semantics. But her subsequent ‘cut-free’ sequent calculus has recently been shown to fail cut-elimination. We present a new cut-free sequent calculus for bi-intuitionistic logic, and prove it sound and complete with respect to its Kripke semantics. Ensuring completeness is complicated by the interaction between intuitionistic implication and dual intuitionistic exclusion, similarly to (...)
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  49. Kathleen Johnson Wu (1988). A Basic Free Logic. Notre Dame Journal of Formal Logic 29 (4):543-552.score: 96.0
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