31 found
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  1.  3
    Cut Elimination Theorem for Non-Commutative Hypersequent Calculus.Andrzej Indrzejczak - 2018 - Bulletin of the Section of Logic 46 (1/2).
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  2.  19
    Linear Time in Hypersequent Framework.Andrzej Indrzejczak - 2016 - Bulletin of Symbolic Logic 22 (1):121-144.
    Hypersequent calculus, developed by A. Avron, is one of the most interesting proof systems suitable for nonclassical logics. Although HC has rather simple form, it increases significantly the expressive power of standard sequent calculi. In particular, HC proved to be very useful in the field of proof theory of various nonclassical logics. It may seem surprising that it was not applied to temporal logics so far. In what follows, we discuss different approaches to formalization of logics of linear frames and (...)
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  3.  23
    Hypersequent Calculi for S5: The Methods of Cut Elimination.Kaja Bednarska & Andrzej Indrzejczak - 2015 - Logic and Logical Philosophy 24 (3):277–311.
  4. Natural Deduction.Andrzej Indrzejczak - 2015
    Natural Deduction Natural Deduction is a common name for the class of proof systems composed of simple and self-evident inference rules based upon methods of proof and traditional ways of reasoning that have been applied since antiquity in deductive practice. The first formal ND systems were independently constructed in the 1930s by G. Gentzen and S. Jaśkowski and … Continue reading Natural Deduction →.
     
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  5.  18
    A Survey of Nonstandard Sequent Calculi.Andrzej Indrzejczak - 2014 - Studia Logica 102 (6):1295-1322.
    The paper is a brief survey of some sequent calculi which do not follow strictly the shape of sequent calculus introduced by Gentzen. We propose the following rough classification of all SC: Systems which are based on some deviations from the ordinary notion of a sequent are called generalised; remaining ones are called ordinary. Among the latter we distinguish three types according to the proportion between the number of primitive sequents and rules. In particular, in one of these types, called (...)
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  6. Generalised Sequent Calculus for Propositional Modal Logics.Andrzej Indrzejczak - 1997 - Logica Trianguli 1:15-31.
    The paper contains an exposition of some non standard approach to gentzenization of modal logics. The first section is devoted to short discussion of desirable properties of Gentzen systems and the short review of various sequential systems for modal logics. Two non standard, cut-free sequent systems are then presented, both based on the idea of using special modal sequents, in addition to usual ones. First of them, GSC I is well suited for nonsymmetric modal logics The second one, GSC II (...)
     
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  7.  14
    Cut-Free Hypersequent Calculus for S4. 3.Andrzej Indrzejczak - 2012 - Bulletin of the Section of Logic 41 (1/2):89-104.
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  8.  3
    Simple Decision Procedure for S5 in Standard Cut-Free Sequent Calculus.Andrzej Indrzejczak - 2017 - Bulletin of the Section of Logic 45 (2).
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  9.  41
    Modal Hybrid Logic.Andrzej Indrzejczak - 2007 - Logic and Logical Philosophy 16 (2-3):147-257.
    This is an extended version of the lectures given during the 12-thConference on Applications of Logic in Philosophy and in the Foundationsof Mathematics in Szklarska Poręba. It contains a surveyof modal hybrid logic, one of the branches of contemporary modal logic. Inthe first part a variety of hybrid languages and logics is presented with adiscussion of expressivity matters. The second part is devoted to thoroughexposition of proof methods for hybrid logics. The main point is to showthat application of hybrid logics (...)
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  10.  21
    Labelled Tableau Calculi for Weak Modal Logics.Andrzej Indrzejczak - 2007 - Bulletin of the Section of Logic 36 (3-4):159-173.
  11.  9
    Natural Deduction System for Tense Logics.Andrzej Indrzejczak - 1994 - Bulletin of the Section of Logic 23 (4):173-179.
  12.  20
    Sequent Calculi for Monotonic Modal Logics.Andrzej Indrzejczak - 2005 - Bulletin of the Section of Logic 34 (3):151-164.
  13.  6
    Decision Procedures for Some Strong Hybrid Logics.Andrzej Indrzejczak & Michał Zawidzki - 2013 - Logic and Logical Philosophy 22 (4):389-409.
    Hybrid logics are extensions of standard modal logics, which significantly increase the expressive power of the latter. Since most of hybrid logics are known to be decidable, decision procedures for them is a widely investigated field of research. So far, several tableau calculi for hybrid logics have been presented in the literature. In this paper we introduce a sound, complete and terminating tableau calculus T H(@,E,D, ♦ −) for hybrid logics with the satisfaction operators, the universal modality, the difference modality (...)
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  14.  7
    Jaśkowski and Gentzen Approaches to Natural Deduction and Related Systems.Andrzej Indrzejczak - 1998 - In Katarzyna Kijania-Placek & Jan Woleński (eds.), The Lvov-Warsaw School and Contemporary Philosophy. Kluwer Academic Publishers. pp. 253--264.
  15.  18
    Suszko's Contribution to the Theory of Nonaxiomatic Proof Systems.Andrzej Indrzejczak - 2009 - Bulletin of the Section of Logic 38 (3/4):151-161.
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  16.  5
    Rule-Generation Theorem and its Applications.Andrzej Indrzejczak - 2019 - Bulletin of the Section of Logic 47 (4):265-281.
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  17.  34
    A Labelled Natural Deduction System for Linear Temporal Logic.Andrzej Indrzejczak - 2003 - Studia Logica 75 (3):345 - 376.
    The paper is devoted to the concise description of some Natural Deduction System (ND for short) for Linear Temporal Logic. The system's distinctive feature is that it is labelled and analytical. Labels convey necessary semantic information connected with the rules for temporal functors while the analytical character of the rules lets the system work as a decision procedure. It makes it more similar to Labelled Tableau Systems than to standard Natural Deduction. In fact, our solution of linearity representation is rather (...)
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  18.  66
    Possible Worlds in Use.Andrzej Indrzejczak - 2011 - Studia Logica 99 (1-3):229-248.
    The paper is a brief survey of the most important semantic constructions founded on the concept of possible world. It is impossible to capture in one short paper the whole variety of the problems connected with manifold applications of possible worlds. Hence, after a brief explanation of some philosophical matters I take a look at possible worlds from rather technical standpoint of logic and focus on the applications in formal semantics. In particular, I would like to focus on the fruitful (...)
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  19.  2
    Cut Elimination in Hypersequent Calculus for Some Logics of Linear Time.Andrzej Indrzejczak - 2019 - Review of Symbolic Logic 12 (4):806-822.
    This is a sequel article to [10] where a hypersequent calculus for some temporal logics of linear frames including Kt4.3 and its extensions for dense and serial flow of time was investigated in detail. A distinctive feature of this approach is that hypersequents are noncommutative, i.e., they are finite lists of sequents in contrast to other hypersequent approaches using sets or multisets. Such a system in [10] was proved to be cut-free HC formalization of respective logics by means of semantical (...)
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  20.  23
    Labelled Analytic Tableaux for S4. 3.Andrzej Indrzejczak - 2002 - Bulletin of the Section of Logic 31 (1):15-26.
  21.  20
    Admissibility of Cut in Congruent Modal Logics.Andrzej Indrzejczak - 2011 - Logic and Logical Philosophy 20 (3):189-203.
    We present a detailed proof of the admissibility of cut in sequent calculus for some congruent modal logics. The result was announced much earlier during the Trends in Logic Conference, Toruń 2006 and the proof for monotonic modal logics was provided already in Indrzejczak [5]. Also some tableau and natural deduction formalizations presented in Indrzejczak [6] and Indrzejczak [7] were based on this result but the proof itself was not published so far. In this paper we are going to fill (...)
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  22.  18
    Correspondence Theory in Proof Theory.Andrzej Indrzejczak - 2008 - Bulletin of the Section of Logic 37 (3/4):171-183.
  23.  6
    Professor Grzegorz Malinowski in Honorem.Andrzej Indrzejczak & Janusz Ciuciura - 2018 - Bulletin of the Section of Logic 46 (1/2).
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  24.  5
    Fregean Description Theory in Proof-Theoretical Setting.Andrzej Indrzejczak - forthcoming - Logic and Logical Philosophy:1.
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  25.  16
    Resolution Based Natural Deduction.Andrzej Indrzejczak - 2002 - Bulletin of the Section of Logic 31 (3):159-170.
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  26. A Survey of Natural Deduction Systems for Modal Logics.Andrzej Indrzejczak - 1999 - Logica Trianguli 3:55-84.
    The paper contains an exposition of standard ND-formalizations for modal logics. For the sake of simplicity, it is limited to propositional monomodal logics because focus is on methods not on logics. Some of the discussed approaches, however, may be easily extended to first order modal logics of different sorts or to multimodal logics . Natural Deduction is understood in the strict sense, explained below; neither Gentzen Sequent Calculus, nor Tableau Systems belong to that group. Moreover, some ND-systems with generalized apparatus, (...)
     
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  27.  17
    Cut-Free Sequent Calculus for S5.Andrzej Indrzejczak - 1996 - Bulletin of the Section of Logic 25 (2):95-102.
  28.  6
    Introduction.Andrzej Indrzejczak - 2014 - Studia Logica 102 (6):1091-1094.
  29. Konferencja Logiki Nieklasyczne - teoria i zastosowania.Andrzej Indrzejczak - 2009 - Ruch Filozoficzny 66 (2).
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  30. Powstanie i ewolucja dedukcji naturalnej.Andrzej Indrzejczak - 2014 - Filozofia Nauki 22 (2):5-20.
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  31. Powstanie i ewolucja rachunków sekwentowych.Andrzej Indrzejczak - 2014 - Filozofia Nauki 22 (4):53-70.
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