Theorem proving for conditional logics: CondLean and GOALD<i>U</i>CK

Olivetti, Nicola; Pozzato, Gian Luca

doi:10.3166/jancl.18.427-473

Cited by 10 publications

(13 citation statements)

References 29 publications

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“…We have similar results also for extensions of CK as shown in Fig. 11 here we have not included GOALDUCK since the most formulas adopted do not belong to the fragments admitting goal-directed proofs [31]. These results show that the performances of NESCOND are encouraging, probably better than the ones of the other existing provers for conditional logics, and this also holds for extensions of CK.…”

Section: Valid Sequentssupporting

confidence: 66%

“…We have compared the performances of NESCOND with the ones of two other provers for conditional logics: CondLean 3.2, implementing labelled sequent calculi [30], and the goal-directed procedure GOALDUCK [31].…”

Section: Nescond Vs Condlean Vs Goalduckmentioning

confidence: 99%

“…We finally provide extensive experimental results by comparing NESCOND with CondLean [30] and GOALDUCK [31], to the best of our knowledge the only existing provers for conditional logics, as well as with CoLoSS [23], a generic-purpose theorem prover for coalgebraic modal logics which can handle also basic conditional logics. Concerning the logic CK+CSO+ID, we have also compared the performances of NESCOND with KLMLean [19], a theorem prover for the cumulative logic C.…”

Section: Introductionmentioning

confidence: 99%

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Nested sequent calculi and theorem proving for normal conditional logics: The theorem prover NESCOND

Olivetti

Pozzato

2015

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Abstract. In this paper we focus on proof methods and theorem proving for normal conditional logics, by describing nested sequent calculi as well as a theorem prover for them. We first present some nested sequent calculi, recently introduced, for the basic conditional logic CK and some of its significant extensions with axioms ID, MP and CEM. We also describe a calculus for the flat fragment of the conditional logic CK+CSO+ID, which corresponds to Kraus, Lehmann and Magidor's cumulative logic C. The calculi are internal, cut-free and analytic. Next, we describe NESCOND, a Prolog implementation of these calculi in the style of leanT A P. We finally present an experimental comparison between our theorem prover NESCOND and other known theorem provers for conditional logics. Our tests show that the performances of NESCOND are promising and in all cases better, with the only exception of systems including CEM, than those ones of the other provers. The program NESCOND, as well as all the Prolog source files, are available at http://www.di.unito.it/∼pozzato/nescond/.

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Section: Valid Sequentssupporting

confidence: 66%

Section: Nescond Vs Condlean Vs Goalduckmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nested sequent calculi and theorem proving for normal conditional logics: The theorem prover NESCOND

Olivetti

Pozzato

2015

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“…We have tested it by running SICStus Prolog 4.0.2 on an Apple MacBook Pro, 2.7 GHz Intel Core i7, 8GB RAM machine. We have compared the performances of NESCOND with the ones of two other provers for conditional logics: CondLean 3.2, implementing labelled sequent calculi [12], and the goal-directed procedure GOALDUCK [13]. We have tested the three provers (i) on randomly generated sequents, obtaining the results shown in Figure 2 and (ii) over a set of valid formulas.…”

Section: Performance Of Nescondmentioning

confidence: 99%

“…The resulting code is therefore simple and compact: the implementation of NESCOND for CK consists of only 6 predicates, 24 clauses and 34 lines of code. We provide experimental results by comparing NESCOND with CondLean [12] and GOALDUCK [13]. Performances of NESCOND are promising, and show that nested sequent calculi are not only a proof theoretical tool, but they can be the basis of efficient theorem proving for conditional logics.…”

Section: Introductionmentioning

confidence: 99%

NESCOND: An Implementation of Nested Sequent Calculi for Conditional Logics

Olivetti

Pozzato

2014

Automated Reasoning

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Abstract. We present NESCOND, a theorem prover for normal conditional logics. NESCOND implements some recently introduced NESted sequent calculi for propositional CONDitional logics CK and some of its significant extensions with axioms ID, MP and CEM. It also deals with the flat fragment of CK+CSO+ID, which corresponds to the logic C introduced by Kraus, Lehmann and Magidor. NESCOND is inspired by the methodology of leanT A P and it is implemented in Prolog. The paper shows some experimental results, witnessing that the performances of NESCOND are promising. The program NESCOND, as well as all the Prolog source files, are available at http://www.di.unito.it/ %7Epozzato/nescond/.

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