Search results for 'Decidability (Mathematical logic' (try it on Scholar)

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  1.  69
    Michał Walicki (2012). Introduction to Mathematical Logic. World Scientific.
    A history of logic -- Patterns of reasoning -- A language and its meaning -- A symbolic language -- 1850-1950 mathematical logic -- Modern symbolic logic -- Elements of set theory -- Sets, functions, relations -- Induction -- Turning machines -- Computability and decidability -- Propositional logic -- Syntax and proof systems -- Semantics of PL -- Soundness and completeness -- First order logic -- Syntax and proof systems of FOL -- Semantics of FOL (...)
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  2.  14
    R. R. Rockingham Gill (1990). Deducibility and Decidability. Routledge.
    The classic results obtained by Gödel, Tarski, Kleene, and Church in the early thirties are the finest flowers of symbolic logic. They are of fundamental importance to those investigations of the foundations of mathematics via the concept of a formal system that were inaugurated by Frege, and of obvious significance to the mathematical disciplines, such as computability theory, that developed from them. Derived from courses taught by the author over several years, this new exposition presents all of the results (...)
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  3.  7
    Andreas Baudisch (ed.) (1980). Decidability and Generalized Quantifiers. Akademie-Verlag.
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  4. Witold Marciszewski (ed.) (2006). Issues of Decidability and Tractability. University of Białystok.
     
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  5.  1
    Bogdan Stanislaw Chlebus (1980). Decidability and Definability Results Concerning Well‐Orderings and Some Extensions of First Order Logic. Mathematical Logic Quarterly 26 (34‐35):529-536.
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  6.  22
    Victor Rodych (1997). Wittgenstein on Mathematical Meaningfulness, Decidability, and Application. Notre Dame Journal of Formal Logic 38 (2):195-224.
    From 1929 through 1944, Wittgenstein endeavors to clarify mathematical meaningfulness by showing how (algorithmically decidable) mathematical propositions, which lack contingent "sense," have mathematical sense in contrast to all infinitistic "mathematical" expressions. In the middle period (1929-34), Wittgenstein adopts strong formalism and argues that mathematical calculi are formal inventions in which meaningfulness and "truth" are entirely intrasystemic and epistemological affairs. In his later period (1937-44), Wittgenstein resolves the conflict between his intermediate strong formalism and his criticism of set theory by requiring (...)
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  7. John Cowles (1982). Baudisch Andreas, Seese Detlef, Tuschik Hans-Peter, and Weese Martin. Decidability and Generalized Quantifiers. Mathematical Research-Mathematische Forschung, Vol. 3. Akademie-Verlag, Berlin 1980, XII + 235 Pp. [REVIEW] Journal of Symbolic Logic 47 (4):907-908.
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  8. A. Prestel (1987). Cherlin Gregory, van den Dries Lou, and Macintyre Angus. Decidability and Undecidability Theorems for PAC-Fields. Bulletin of the American Mathematical Society, N.S. Vol. 4 , Pp. 101–104. [REVIEW] Journal of Symbolic Logic 52 (2):568.
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  9. Dirk Siefkes (1972). Rabin Michael O.. Decidability of Second-Order Theories and Automata on Infinite Trees. Bulletin of the American Mathematical Society, Vol. 74 , Pp. 1025–1029.Rabin Michael O.. Decidability of Second-Order Theories and Automata on Infinite Trees. Transactions of the American Mathematical Society, Vol. 141 , Pp. 1–35. [REVIEW] Journal of Symbolic Logic 37 (3):618-619.
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  10. Ann Yasuhara (1972). Kuznecov A. V.. Undecidability of the General Problems of Completeness, Decidability and Equivalence for Propositional Calculi. English Translation of XXXVII 772 by E. Mendelson. American Mathematical Society Translations, Ser. 2 Vol. 59 , Pp. 56–72. [REVIEW] Journal of Symbolic Logic 37 (4):756-757.
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  11. Egon Boerger (1997). The Classical Decision Problem. Springer.
     
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  12. Robert Sochacki (2010). Metody Refutacyjne W Badaniach Nad Systemami Logicznymi. Uniwersytet Opolski.
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  13.  6
    Frank Wolter (1996). Tense Logic Without Tense Operators. Mathematical Logic Quarterly 42 (1):145-171.
    We shall describe the set of strongly meet irreducible logics in the lattice ϵLin.t of normal tense logics of weak orderings. Based on this description it is shown that all logics in ϵLin.t are independently axiomatizable. Then the description is used in order to investigate tense logics with respect to decidability, finite axiomatizability, axiomatization problems and completeness with respect to Kripke semantics. The main tool for the investigation is a translation of bimodal formulas into a language talking about partitions (...)
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  14. Z. Ognjanovic & Z. Markovic (2003). A Probabilistic Extension of Intuitionistic Logic. Mathematical Logic Quarterly 49 (4):415.
    We introduce a probabilistic extension of propositional intuitionistic logic. The logic allows making statements such as P≥sα, with the intended meaning “the probability of truthfulness of α is at least s”. We describe the corresponding class of models, which are Kripke models with a naturally arising notion of probability, and give a sound and complete infinitary axiomatic system. We prove that the logic is decidable.
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  15.  58
    Andrzej Grzegorczyk (2005). Undecidability Without Arithmetization. Studia Logica 79 (2):163 - 230.
    In the present paper the well-known Gödels – Churchs argument concerning the undecidability of logic (of the first order functional calculus) is exhibited in a way which seems to be philosophically interestingfi The natural numbers are not used. (Neither Chinese Theorem nor other specifically mathematical tricks are applied.) Only elementary logic and very simple set-theoretical constructions are put into the proof. Instead of the arithmetization I use the theory of concatenation (formalized by Alfred Tarski). This theory proves to (...)
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  16.  3
    Michael Zakharyaschevm & Alexander Alekseev (1995). All Finitely Axiomatizable Normal Extensions of K4.3 Are Decidable. Mathematical Logic Quarterly 41 (1):15-23.
    We use the apparatus of the canonical formulas introduced by Zakharyaschev [10] to prove that all finitely axiomatizable normal modal logics containing K4.3 are decidable, though possibly not characterized by classes of finite frames. Our method is purely frame-theoretic. Roughly, given a normal logic L above K4.3, we enumerate effectively a class of frames with respect to which L is complete, show how to check effectively whether a frame in the class validates a given formula, and then apply a (...)
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  17.  6
    Matteo Bianchi (2013). First-Order Nilpotent Minimum Logics: First Steps. Archive for Mathematical Logic 52 (3-4):295-316.
    Inspired by the work done by Baaz et al. (Ann Pure Appl Log 147(1–2): 23–47, 2007; Lecture Notes in Computer Science, vol 4790/2007, pp 77–91, 2007) for first-order Gödel logics, we investigate Nilpotent Minimum logic NM. We study decidability and reciprocal inclusion of various sets of first-order tautologies of some subalgebras of the standard Nilpotent Minimum algebra, establishing also a connection between the validity in an NM-chain of certain first-order formulas and its order type. Furthermore, we analyze axiomatizability, (...)
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  18.  33
    Richard Zach (1999). Completeness Before Post: Bernays, Hilbert, and the Development of Propositional Logic. Bulletin of Symbolic Logic 5 (3):331-366.
    Some of the most important developments of symbolic logic took place in the 1920s. Foremost among them are the distinction between syntax and semantics and the formulation of questions of completeness and decidability of logical systems. David Hilbert and his students played a very important part in these developments. Their contributions can be traced to unpublished lecture notes and other manuscripts by Hilbert and Bernays dating to the period 1917-1923. The aim of this paper is to describe these (...)
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  19.  4
    Takahito Aoto & Hiroyuki Shirasu (1999). On the Finite Model Property of Intuitionistic Modal Logics Over MIPC. Mathematical Logic Quarterly 45 (4):435-448.
    MIPC is a well-known intuitionistic modal logic of Prior and Bull . It is shown that every normal intuitionistic modal logic L over MIPC has the finite model property whenever L is Kripke-complete and universal.
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  20.  11
    Nikolaos Galatos & James G. Raftery (2004). Adding Involution to Residuated Structures. Studia Logica 77 (2):181 - 207.
    Two constructions for adding an involution operator to residuated ordered monoids are investigated. One preserves integrality and the mingle axiom x 2x but fails to preserve the contraction property xx 2. The other has the opposite preservation properties. Both constructions preserve commutativity as well as existent nonempty meets and joins and self-dual order properties. Used in conjunction with either construction, a result of R.T. Brady can be seen to show that the equational theory of commutative distributive residuated lattices (without involution) (...)
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  21.  17
    Ian Hodkinson (2002). Monodic Packed Fragment with Equality is Decidable. Studia Logica 72 (2):185-197.
    We prove decidability of satisfiability of sentences of the monodic packed fragment of first-order temporal logic with equality and connectives Until and Since, in models with various flows of time and domains of arbitrary cardinality. We also prove decidability over models with finite domains, over flows of time including the real order.
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  22.  22
    Dimiter Vakarelov (2005). Nelson's Negation on the Base of Weaker Versions of Intuitionistic Negation. Studia Logica 80 (2-3):393-430.
    Constructive logic with Nelson negation is an extension of the intuitionistic logic with a special type of negation expressing some features of constructive falsity and refutation by counterexample. In this paper we generalize this logic weakening maximally the underlying intuitionistic negation. The resulting system, called subminimal logic with Nelson negation, is studied by means of a kind of algebras called generalized N-lattices. We show that generalized N-lattices admit representation formalizing the intuitive idea of refutation by means (...)
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  23. Alan Ross Anderson, Ruth Barcan Marcus, R. M. Martin & Frederic B. Fitch (eds.) (1975). The Logical Enterprise. Yale University Press.
    Metaphysics and language: Quine, W. V. O. On the individuation of attributes. Körner, S. On some relations between logic and metaphysics. Marcus, R. B. Does the principle of substitutivity rest on a mistake? Van Fraassen, B. C. Platonism's pyrrhic victory. Martin, R. M. On some prepositional relations. Kearns, J. T. Sentences and propositions.--Basic and combinatorial logic: Orgass, R. J. Extended basic logic and ordinal numbers. Curry, H. B. Representation of Markov algorithms by combinators.--Implication and consistency: Anderson, A. (...)
     
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  24.  14
    Pavel Naumov (2005). On Modal Logics of Partial Recursive Functions. Studia Logica 81 (3):295 - 309.
    The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to partial recursive function type constructor under the above interpretation. The cases of deterministic and non-deterministic functions are considered and for both of them semantically complete modal logics are described and decidability of these logics is established.
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  25.  27
    Konstantinos Georgatos (1997). Knowledge on Treelike Spaces. Studia Logica 59 (2):271-301.
    This paper presents a bimodal logic for reasoning about knowledge during knowledge acquisitions. One of the modalities represents (effort during) non-deterministic time and the other represents knowledge. The semantics of this logic are tree-like spaces which are a generalization of semantics used for modeling branching time and historical necessity. A finite system of axiom schemes is shown to be canonically complete for the formentioned spaces. A characterization of the satisfaction relation implies the small model property and decidability (...)
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  26.  13
    Wojciech Buszkowski (2007). Type Logics and Pregroups. Studia Logica 87 (2-3):145 - 169.
    We discuss the logic of pregroups, introduced by Lambek [34], and its connections with other type logics and formal grammars. The paper contains some new ideas and results: the cut-elimination theorem and a normalization theorem for an extended system of this logic, its P-TIME decidability, its interpretation in L1, and a general construction of (preordered) bilinear algebras and pregroups whose universe is an arbitrary monoid.
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  27.  2
    Mohammad Ardeshir & Rasoul Ramezanian (2009). Decidability and Specker Sequences in Intuitionistic Mathematics. Mathematical Logic Quarterly 55 (6):637-648.
    A bounded monotone sequence of reals without a limit is called a Specker sequence. In Russian constructive analysis, Church's Thesis permits the existence of a Specker sequence. In intuitionistic mathematics, Brouwer's Continuity Principle implies it is false that every bounded monotone sequence of real numbers has a limit. We claim that the existence of Specker sequences crucially depends on the properties of intuitionistic decidable sets. We propose a schema about intuitionistic decidability that asserts “there exists an intuitionistic enumerable set (...)
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  28.  1
    Qin Jun (1992). An Elementary System as and its Semi‐Completeness and Decidability. Mathematical Logic Quarterly 38 (1):305-320.
    The author establishes an elementary system AS which contains functions +, ≐ and a constant 0 and then proves the semi-completeness and the decidability of AS, using the theory of systems of inequalities.
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  29.  1
    Armin Hemmerling (2003). Approximate Decidability in Euclidean Spaces. Mathematical Logic Quarterly 49 (1):34-56.
    We study concepts of decidability for subsets of Euclidean spaces ℝk within the framework of approximate computability . A new notion of approximate decidability is proposed and discussed in some detail. It is an effective variant of F. Hausdorff's concept of resolvable sets, and it modifies and generalizes notions of recursivity known from computable analysis, formerly used for open or closed sets only, to more general types of sets. Approximate decidability of sets can equivalently be expressed by (...)
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  30. Carlo Toffalori & S. Cittadini (2002). Comparing First Order Theories of Modules Over Group Rings II: Decidability: Decidability. Mathematical Logic Quarterly 48 (4):483-498.
    We consider R-torsionfree modules over group rings RG, where R is a Dedekind domain and G is a finite group. In the first part of the paper [4] we compared the theory T of all R-torsionfree RG-modules and the theory T0 of RG-lattices , and we realized that they are almost always different. Now we compare their behaviour with respect to decidability, when RG-lattices are of finite, or wild representation type.
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  31. Johannes Brandl & Peter M. Sullivan (eds.) (1998). New Essays on the Philosophy of Michael Dummett. Rodopi.
    Ever since the publication of 'Truth' in 1959 Sir Michael Dummett has been acknowledged as one of the most profoundly creative and influential of contemporary philosophers. His contributions to the philosophy of thought and language, logic, the philosophy of mathematics, and metaphysics have set the terms of some of most fruitful discussions in philosophy. His work on Frege stands unparalleled, both as landmark in the history of philosophy and as a deep reflection on the defining commitments of the analytic (...)
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  32. Moritz Pasch (2010). Essays on the Foundations of Mathematics. Springer.
    Translator's introduction -- Fundamental questions of geometry -- The decidability requirement -- The origin of the concept of number -- Implicit definition and the proper grounding of mathematics -- Rigid bodies in geometry -- Prelude to geometry : the essential ideas -- Physical and mathematical geometry -- Natural geometry -- The concept of the differential -- Reflections on the proper grounding of mathematics I -- Concepts and proofs in mathematics -- Dimension and space in mathematics -- Reflections on the (...)
     
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  33. Eugenio G. Omodeo, Franco Parlamento & Alberto Policriti (1996). Decidability of ∀*∀‐Sentences in Membership Theories. Mathematical Logic Quarterly 42 (1):41-58.
    The problem is addressed of establishing the satisfiability of prenex formulas involving a single universal quantifier, in diversified axiomatic set theories. A rather general decision method for solving this problem is illustrated through the treatment of membership theories of increasing strength, ending with a subtheory of Zermelo-Fraenkel which is already complete with respect to the ∀*∀ class of sentences. NP-hardness and NP-completeness results concerning the problems under study are achieved and a technique for restricting the universal quantifier is presented.
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  34.  2
    Paola D'Aquino & Giuseppina Terzo (2007). A Note on the Decidability of Exponential Terms. Mathematical Logic Quarterly 53 (3):306-310.
    In this paper we prove, modulo Schanuel's Conjecture, that there are algorithms which decide if two exponential polynomials in π are equal in ℝ and if two exponential polynomials in π and i coincide in ℂ.
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  35.  1
    Miklós Erdélyi‐Szabó (1997). Decidability in the Constructive Theory of Reals as an Ordered ℚ‐Vectorspace. Mathematical Logic Quarterly 43 (3):343-354.
    We show that various fragments of the intuitionistic/constructive theory of the reals are decidable.
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  36.  4
    Luca Viganò (2000). Labelled Non-Classical Logics. Kluwer Academic Publishers.
    The subject of Labelled Non-Classical Logics is the development and investigation of a framework for the modular and uniform presentation and implementation of non-classical logics, in particular modal and relevance logics. Logics are presented as labelled deduction systems, which are proved to be sound and complete with respect to the corresponding Kripke-style semantics. We investigate the proof theory of our systems, and show them to possess structural properties such as normalization and the subformula property, which we exploit not only to (...)
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  37.  47
    Dov M. Gabbay (ed.) (2003). Many-Dimensional Modal Logics: Theory and Applications. Elsevier North Holland.
    Modal logics, originally conceived in philosophy, have recently found many applications in computer science, artificial intelligence, the foundations of mathematics, linguistics and other disciplines. Celebrated for their good computational behaviour, modal logics are used as effective formalisms for talking about time, space, knowledge, beliefs, actions, obligations, provability, etc. However, the nice computational properties can drastically change if we combine some of these formalisms into a many-dimensional system, say, to reason about knowledge bases developing in time or moving objects. To study (...)
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  38.  11
    Jonas De Vuyst (2013). Dynamic Tableaux for Dynamic Modal Logics. Dissertation, Vrije Universiteit Brussel
    In this dissertation we present proof systems for several modal logics. These proof systems are based on analytic (or semantic) tableaux. -/- Modal logics are logics for reasoning about possibility, knowledge, beliefs, preferences, and other modalities. Their semantics are almost always based on Saul Kripke’s possible world semantics. In Kripke semantics, models are represented by relational structures or, equivalently, labeled graphs. Syntactic formulas that express statements about knowledge and other modalities are evaluated in terms of such models. -/- This dissertation (...)
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  39.  25
    Mojżesz Presburger & Dale Jabcquette (1991). On the Completeness of a Certain System of Arithmetic of Whole Numbers in Which Addition Occurs as the Only Operation. History and Philosophy of Logic 12 (2):225-233.
    Presburger's essay on the completeness and decidability of arithmetic with integer addition but without multiplication is a milestone in the history of mathematical logic and formal metatheory. The proof is constructive, using Tarski-style quantifier elimination and a four-part recursive comprehension principle for axiomatic consequence characterization. Presburger's proof for the completeness of first order arithmetic with identity and addition but without multiplication, in light of the restrictive formal metatheorems of Gödel, Church, and Rosser, takes the foundations of arithmetic in (...)
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  40.  5
    Pierluigi Minari (2004). Analytic Combinatory Calculi and the Elimination of Transitivity. Archive for Mathematical Logic 43 (2):159-191.
    We introduce, in a general setting, an ‘‘analytic’’ version of standard equational calculi of combinatory logic. Analyticity lies on the one side in the fact that these calculi are characterized by the presence of combinatory introduction rules in place of combinatory axioms, and on the other side in that the transitivity rule proves to be eliminable. Apart from consistency, which follows immediately, we discuss other almost direct consequences of analyticity and the main transitivity elimination theorem; in particular the Church−Rosser (...)
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  41.  9
    Silvio Valentini (1996). Decidability in Intuitionistic Type Theory is Functionally Decidable. Mathematical Logic Quarterly 42 (1):300-304.
    In this paper we show that the usual intuitionistic characterization of the decidability of the propositional function B prop [x : A], i. e. to require that the predicate ∨ ¬ B) is provable, is equivalent, when working within the framework of Martin-Löf's Intuitionistic Type Theory, to require that there exists a decision function ψ: A → Boole such that = Booletrue) ↔ B). Since we will also show that the proposition x = Booletrue [x: Boole] is decidable, we (...)
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  42. Carlo Toffalori (1996). Decidability for ℤ[G]‐Modules When G is Cyclic of Prime Order. Mathematical Logic Quarterly 42 (1):369-378.
    We consider the decision problem for modules over a group ring ℤ[G], where G is a cyclic group of prime order. We show that it reduces to the same problem for a class of certain abelian structures, and we obtain some partial decidability results for this class.
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  43.  24
    Stéphane Demri & Dov Gabbay (2000). On Modal Logics Characterized by Models with Relative Accessibility Relations: Part I. Studia Logica 65 (3):323-353.
    This work is divided in two papers (Part I and Part II). In Part I, we study a class of polymodal logics (herein called the class of "Rare-logics") for which the set of terms indexing the modal operators are hierarchized in two levels: the set of Boolean terms and the set of terms built upon the set of Boolean terms. By investigating different algebraic properties satisfied by the models of the Rare-logics, reductions for decidability are established by faithfully translating (...)
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  44.  11
    Stéphane Demri & Dov Gabbay (2000). On Modal Logics Characterized by Models with Relative Accessibility Relations: Part II. Studia Logica 66 (3):349-384.
    This work is divided in two papers (Part I and Part II). In Part I, we introduced the class of Rare-logics for which the set of terms indexing the modal operators are hierarchized in two levels: the set of Boolean terms and the set of terms built upon the set of Boolean terms. By investigating different algebraic properties satisfied by the models of the Rare-logics, reductions for decidability were established by faithfully translating the Rare-logics into more standard modal logics (...)
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  45.  53
    Marc Dymetman (1998). Group Theory and Computational Linguistics. Journal of Logic, Language and Information 7 (4):461-497.
    There is currently much interest in bringing together the tradition of categorial grammar, and especially the Lambek calculus, with the recent paradigm of linear logic to which it has strong ties. One active research area is designing non-commutative versions of linear logic (Abrusci, 1995; Retoré, 1993) which can be sensitive to word order while retaining the hypothetical reasoning capabilities of standard (commutative) linear logic (Dalrymple et al., 1995). Some connections between the Lambek calculus and computations in groups (...)
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  46. Sergei Artëmov & Vladimir Krupski (1996). Data Storage Interpretation of Labeled Modal Logic. Annals of Pure and Applied Logic 78 (1-3):57-71.
    We introduce reference structures — a basic mathematical model of a data organization capable of storing and utilizing information about its addresses. A propositional labeled modal language is used as a specification and programming language for reference structures; the satisfiability algorithm for modal language gives a method of building and optimizing reference structures satisfying a given formula. Corresponding labeled modal logics are presented, supplied with cut free axiomatizations, completeness and decidability theorems are proved. Initialization of typed variables in some (...)
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  47.  2
    Christian Thiel (1988). Die kontroverse um die intuitionistische logik vor ihrer axiomatisierung durch heyting im jahre 1930. History and Philosophy of Logic 9 (1):67-75.
    Brouwer's criticism of mathematical proofs making essential use of the tertium non datur had a surprisingly late response in logical circles. Among the diverse reactions in the mid 1920s and early 1930s, it is possible to delimit a coherent body of opinions on these questions: (1) whether Brouwer's denial of the tertium non datur meant only the abandonment of this classical law or, beyond that, the affirmation of its negation; (2) whether one or both of these alternatives were logically inconsistent; (...)
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  48.  47
    Greg Restall (2000). An Introduction to Substructural Logics. Routledge.
    This book introduces an important group of logics that have come to be known under the umbrella term 'susbstructural'. Substructural logics have independently led to significant developments in philosophy, computing and linguistics. _An Introduction to Substrucural Logics_ is the first book to systematically survey the new results and the significant impact that this class of logics has had on a wide range of fields.The following topics are covered: * Proof Theory * Propositional Structures * Frames * Decidability * Coda (...)
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  49.  4
    Andreas Baudisch (1982). Decidability and Stability of Free Nilpotent Lie Algebras and Free Nilpotent P-Groups of Finite Exponent. Annals of Mathematical Logic 23 (1):1-25.
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  50. Dov M. Gabbay (1975). Decidability Results in Non-Classical Logics. Annals of Mathematical Logic 8 (3):237-295.
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