Automated Support for the Investigation of Paraconsistent and Other Logics

Ciabattoni, Agata; Lahav, Ori; Spendier, Lara; Zamansky, Anna

doi:10.1007/978-3-642-35722-0_9

Cited by 9 publications

(6 citation statements)

References 9 publications

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“…Furthermore, we show that if the PNmatrix constructed for H contains no empty sets, then the corresponding sequent calculus is analytic, as it enjoys a certain generalized subformula property. This article extends the results of Ciabattoni et al [2013]. However, in contrast to Ciabattoni et al [2013], we allow here axioms with possible nesting of unary connectives of any fixed depth.…”

Section: Introductionmentioning

confidence: 80%

“…This article extends the results of Ciabattoni et al [2013]. However, in contrast to Ciabattoni et al [2013], we allow here axioms with possible nesting of unary connectives of any fixed depth. This allows us to capture, for example, the logics investigated in Kamide [2013] that could not be dealt with in our the previous work.…”

Section: Introductionmentioning

confidence: 80%

“…The family of Hilbert calculi handled in Ciabattoni et al [2013] is properly contained in H. The subformulas in the axiom schemata of Ax L can indeed be prefixed by any finite sequence of connectives from U L , and not only by one (or, in particular cases, by two) as in the axioms considered in Ciabattoni et al [2013].…”

Section: The Family Hmentioning

confidence: 99%

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Taming Paraconsistent (and Other) Logics

Ciabattoni

Lahav

Spendier

et al. 2014

ACM Trans. Comput. Logic

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We develop a fully algorithmic approach to "taming" logics expressed Hilbert style, that is, reformulating them in terms of analytic sequent calculi and useful semantics. Our approach applies to Hilbert calculi extending the positive fragment of propositional classical logic with axioms of a certain general form that contain new unary connectives. Our work encompasses various results already obtained for specific logics. It can be applied to new logics, as well as to known logics for which an analytic calculus or a useful semantics has so far not been available. A Prolog implementation of the method is described.

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Section: Introductionmentioning

confidence: 80%

Section: Introductionmentioning

confidence: 80%

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Taming Paraconsistent (and Other) Logics

Ciabattoni

Lahav

Spendier

et al. 2014

ACM Trans. Comput. Logic

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“…We believe that these results will help produce efficient tools for automated reasoning with inconsistency, eventually making LFIs a more appealing formalism for reasoning under uncertainty. A first step in this direction has been recently taken in [23]: an algorithm for a fully automatic generation of non-deterministic semantics and cut-free sequent calculi for practically all the C-systems studied in this paper (and many more) has been implemented there in Prolog.…”

Section: Conclusion and Further Researchmentioning

confidence: 99%

Cut-free sequent calculi for C-systems with generalized finite-valued semantics

Avron¹,

Konikowska²,

Zamansky³

2012

Journal of Logic and Computation

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In [5], a general method was developed for generating cut-free ordinary sequent calculi for logics that can be characterized by finite-valued semantics based on non-deterministic matrices (Nmatrices). In this paper, a substantial step towards automation of paraconsistent reasoning is made by applying that method to a certain crucial family of thousands of paraconsistent logics, all belonging to the class of C-systems. For that family, the method produces in a modular way uniform Gentzen-type rules corresponding to a variety of axioms considered in the literature.

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“…Similarly, [13] uses labels to capture first-order frame conditions over normal modal logics definable by geometric sequents. Finally, [6] translates between paraconsistent logics and sequent calculi in a similar way, using different syntactical formats (and construct cut-free sequent systems via non-deterministic semantics). We are not aware of any translations between modal axioms and logical rules for pure sequent calculi or any formal impossibility results.…”

Section: Introductionmentioning

confidence: 99%

Correspondence between Modal Hilbert Axioms and Sequent Rules with an Application to S5

Lellmann

Pattinson

2013

Lecture Notes in Computer Science

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Abstract. Which modal logics can be 'naturally' captured by a sequent system? Clearly, this question hinges on what one believes to be natural, i.e. which format of sequent rules one is willing to accept. This paper studies the relationship between the format of sequent rules and the corresponding syntactical shape of axioms in an equivalent Hilbert-system. We identify three different such formats, the most general of which captures most logics in the S5-cube. The format is based on restricting the context in rule premises and the correspondence is established by translating axioms into rules of our format and vice versa. As an application we show that there is no set of sequent rules of this format which is sound and cut-free complete for S5 and for which cut elimination can be shown by the standard permutation-of-rules argument.

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Automated Support for the Investigation of Paraconsistent and Other Logics

Cited by 9 publications

References 9 publications

Taming Paraconsistent (and Other) Logics

Taming Paraconsistent (and Other) Logics

Cut-free sequent calculi for C-systems with generalized finite-valued semantics

Correspondence between Modal Hilbert Axioms and Sequent Rules with an Application to S5

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