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14
On the PolynomialSpace Completeness of Intuitionistic Propositional Logic
, 2003
"... The original publication is available at www.springerlink.com. We present an alternative, purely semantical and relatively simple, proof of the Statman’s result that both intuitionistic propositional logic and its implicational fragment are PSPACEcomplete. 1 ..."
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Cited by 6 (1 self)
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The original publication is available at www.springerlink.com. We present an alternative, purely semantical and relatively simple, proof of the Statman’s result that both intuitionistic propositional logic and its implicational fragment are PSPACEcomplete. 1
On Modal Systems with Rosser Modalities
"... Sufficiently strong axiomatic theories allow for the construction of selfreferential sentences, i.e. sentences saying something about themselves. After the Gödel’s paper on incompleteness (Gödel, 1931) the selfreference method found further applications—some are listed below—and became even more ..."
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Sufficiently strong axiomatic theories allow for the construction of selfreferential sentences, i.e. sentences saying something about themselves. After the Gödel’s paper on incompleteness (Gödel, 1931) the selfreference method found further applications—some are listed below—and became even more
Weak Theories and Essential Incompleteness
"... undecidability This paper is motivated by the following question: what is the weakest theory that is essentially incomplete or essentially undecidable? An axiomatic theory T is complete if it is consistent and for every sentence ..."
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undecidability This paper is motivated by the following question: what is the weakest theory that is essentially incomplete or essentially undecidable? An axiomatic theory T is complete if it is consistent and for every sentence
The Decision Problem of Provability Logic with Only One Atom
, 2003
"... The original publication is available at www.springerlink.com. The decision problem for provability logic remains PSPACEcomplete even if the number of propositional atoms is restricted to one. In some cases the set of all tautologies of a modal logic is in coNP. An example of a logic like that is t ..."
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Cited by 1 (0 self)
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The original publication is available at www.springerlink.com. The decision problem for provability logic remains PSPACEcomplete even if the number of propositional atoms is restricted to one. In some cases the set of all tautologies of a modal logic is in coNP. An example of a logic like that is the wellknown S5. However, most of the traditional modal systems, including S4 and T, have PSPACEcomplete decision problem. So one can say that adding modalities to the language of classical propositional logic does increase algorithmic complexity — not a surprising paradigm. The methods for constructing a polynomial space decision procedure and for proving PSPACEcompleteness of a modal logic can be learnt from R. Ladner’s paper [Lad77]. Provability logic GL is not mentioned in [Lad77], but it is not difficult to verify that GL has PSPACEcomplete decision problem as well. In this paper we go farther and use Ladner’s methods to show that the decision problem of GL is PSPACEcomplete even if the number of propositional atoms used to build modal formulas is restricted to one. This fact can be interpreted as saying that, in case of provability logic, allowing more than one atom does not increase the expressive power of the language. The structure of the present paper is similar to that of our [ ˇ Sve03] where an alternative simple proof of R. Statman’s result concerning PSPACEcompleteness of intuitionistic propositional logic is presented. Modal formulas are built up from propositional atoms and the symbol ⊥ for falsity using logical connectives and a unary symbol ✷ for necessity. We use ✸A
On Interpretability in the Theory of Concatenation
, 2008
"... A preprint We present a relatively simple proof, alternative to A. Visser’s proof in his Growing commas article, that Robinson arithmetic is interpretable in the theory of concatenation TC. 1 ..."
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A preprint We present a relatively simple proof, alternative to A. Visser’s proof in his Growing commas article, that Robinson arithmetic is interpretable in the theory of concatenation TC. 1
On Interplay of Quantifiers in GödelDummett Fuzzy Logics
, 2005
"... The original publication is available at www.springerlink.com. Axiomatization of GödelDummett predicate logics S2G, S3G, and PG, where PG is the weakest logic in which all prenex operations are sound, and the relationships of these logics to logics known from the literature are discussed. Examples ..."
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The original publication is available at www.springerlink.com. Axiomatization of GödelDummett predicate logics S2G, S3G, and PG, where PG is the weakest logic in which all prenex operations are sound, and the relationships of these logics to logics known from the literature are discussed. Examples of nonprenexable formulas are given for those logics where some prenex operation is not available. Interexpressibility of quantifiers is explored for each of the considered logics. 1
Logic Group 'reprint Series
, 1995
"... Abstract. For finitely axiomatized sequential theories F and reflexive theories R, we give a characterization of the relation `F interprets R ' in terms of provability of restricted consistency statements on cuts. This characterization is used in a proof that the set of IIl (as well as E1) sent ..."
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Abstract. For finitely axiomatized sequential theories F and reflexive theories R, we give a characterization of the relation `F interprets R ' in terms of provability of restricted consistency statements on cuts. This characterization is used in a proof that the set of IIl (as well as E1) sentences yr s.t. GB interprets ZF + Tr is E3complete. Relative interpretability among formal theories has been particularly well studied in two specific cases: that of finitely axiomatized sequential theories (see Smorynski [14], Pudlak [11], Visser [16] etc.), and of reflexive, esp. essentially reflexive theories (see Lindstrom [7], [8] etc.). We have nice characterizations of the interpretability relation between a pair of theories
Intuitionistic implication makes model checking Phard. ArXiv eprints
, 1107
"... Abstract. We investigate the complexity of the model checking problem for intuitionistic and modal propositional logics over transitive Kripke models. More specific, we consider intuitionistic logic IPC, basic propositional logic BPL, formal propositional logic FPL, and Jankov’s logic KC. We show th ..."
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Abstract. We investigate the complexity of the model checking problem for intuitionistic and modal propositional logics over transitive Kripke models. More specific, we consider intuitionistic logic IPC, basic propositional logic BPL, formal propositional logic FPL, and Jankov’s logic KC. We show that the model checking problem is Pcomplete for the implicational fragments of all these intuitionistic logics. For BPL and FPL we reach Phardness even on the implicational fragment with only one variable. The same hardness results are obtained for the strictly implicational fragments of their modal companions. Moreover, we investigate whether formulas with less variables and additional connectives make model checking easier. Whereas for variable free formulas outside of the implicational fragment, FPL model checking is shown to be in LOGCFL, the problem remains Pcomplete for BPL. 1.
Structures and Deduction  the Quest for the Essence of Proofs (satellite workshop of ICALP 2005)
, 2005
"... Derivations, Equational Logic and Interpolation p. 173 Elaine Pimentel, Simona Ronchi della Rocca and Luca Roversi: Intersection Types: a ProofTheoretical Approach p. 189 Joao Rasga: A Cut Elimination in Propositional Based Logics p. 205 Beyond Deduction Modulo Claude Kirchner INRIA & LO ..."
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Derivations, Equational Logic and Interpolation p. 173 Elaine Pimentel, Simona Ronchi della Rocca and Luca Roversi: Intersection Types: a ProofTheoretical Approach p. 189 Joao Rasga: A Cut Elimination in Propositional Based Logics p. 205 Beyond Deduction Modulo Claude Kirchner INRIA & LORIA Nancy, France From Deep Inference to Proof Nets Universitat des Saarlandes  Informatik  Programmiersysteme Postfach 15 11 50  66041 Saarbrucken  Germany http://www.ps.unisb.de/~lutz Abstract. This paper shows how derivations in (a variation of) SKS can be translated into proof nets. Since an SKS derivation contains more information about a proof than the corresponding proof net, we observe a loss of information which can be understood as "eliminating bureaucracy ". Technically this is achieved by cut reduction on proof nets. As an intermediate step between the two extremes, SKS derivations and proof nets, we will see nets representing derivations in "Formalism A".
Results 1  10
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