PRONOM: Proof-Search and Countermodel Generation for Non-normal Modal Logics

Dalmonte, Tiziano; Negri, Sara; Olivetti, Nicola; Pozzato, Gian Luca

doi:10.1007/978-3-030-35166-3_12

Cited by 3 publications

(4 citation statements)

References 19 publications

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“…Finally we wish to study the formal relation with other recent calculi in the literature such as [4,13] in the form of mutual simulation. We also think of implementing our calculi and comparing them with the theorem prover proposed recently in [6].…”

Section: Resultsmentioning

confidence: 99%

Countermodel Construction via Optimal Hypersequent Calculi for Non-normal Modal Logics

Dalmonte

Lellmann

Olivetti

et al. 2019

Logical Foundations of Computer Science

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We develop semantically-oriented calculi for the cube of nonnormal modal logics and some deontic extensions. The calculi manipulate hypersequents and have a simple semantic interpretation. Their main feature is that they allow for direct countermodel extraction. Moreover they provide an optimal decision procedure for the respective logics. They also enjoy standard proof-theoretical properties, such as a syntactical proof of cut-admissibility.

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Section: Resultsmentioning

confidence: 99%

Countermodel Construction via Optimal Hypersequent Calculi for Non-normal Modal Logics

Dalmonte

Lellmann

Olivetti

et al. 2019

Logical Foundations of Computer Science

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“…The implementation of the calculi for extensions of E is very similar:given the modularity of the calculi LSE * [5], each system is obtained by just adding clauses for both the predicates terminating_proof _search and build_saturate_branch corresponding to the axioms/rules specifically tailored for the extensions under consideration. However, with the exceptions of two files 4 containing some utilities and the definitions of the connectives, that are common to all the systems, we provide a different Prolog file for each system of the cube. This choice is justified by two reasons: first of all readiness of the code: one may be interested only in one specific system, wishing to have all the rules in a stand-alone file.…”

Section: Extensions Of Ementioning

confidence: 99%

Proof-search and countermodel generation for non-normal modal logics: The theorem prover PRONOM

Dalmonte

Negri

Olivetti

et al. 2021

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In this work we present PRONOM, a theorem prover and countermodel generator for non-normal modal logics. PRONOM implements some labelled sequent calculi recently introduced for the basic system E and its extensions with axioms M, N, and C based on bi-neighbourhood semantics. PRONOM is inspired by the methodology of leanTAP and is implemented in Prolog. When a modal formula is valid, then PRONOM computes a proof (a closed tree) in the labelled calculi having a sequent with an empty left-hand side and containing only that formula on the right-hand side as a root, otherwise PRONOM is able to extract a model falsifying it from an open, saturated branch. The paper shows some experimental results, witnessing that the performances of PRONOM are promising.

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“…We have compared the performance of HYPNO with those of the prover PRONOM [5], which deals with the same set of logics, obtaining promising results. We have tested it by running SWI-Prolog, version 7.6.4, on an Apple MacBook Pro, 2.7 GHz Intel Core i7, 8 GB RAM machine.…”

Section: Performance Of Hypnomentioning

confidence: 99%

“…In [11] it is presented a Prolog implementation of a NNML containing both the [∀∀] and the [∃∀] modality; its [∃∀] fragment coincides with the logic EM, also covered by HYPNO. Finally in [5] it is presented PRONOM, a theorem prover for the whole range of NNMLs, which implements labelled sequent calculi in [6]; PRONOM provides both proofs and countermodels in the mentioned bi-neighbourhood semantics.…”

Section: Introductionmentioning

confidence: 99%

HYPNO: Theorem Proving with Hypersequent Calculi for Non-normal Modal Logics (System Description)

Dalmonte¹,

Olivetti²,

Pozzato³

2020

Automated Reasoning

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We present HYPNO (HYpersequent Prover for NOn-normal modal logics), a Prolog-based theorem prover and countermodel generator for non-normal modal logics. HYPNO implements some hypersequent calculi recently introduced for the basic system E and its extensions with axioms M, N, and C. It is inspired by the methodology of leanT A P , so that it does not make use of any ad-hoc control mechanism. Given a formula, HYPNO provides either a proof in the calculus or a countermodel, directly built from an open saturated hypersequent. Preliminary experimental results show that the performances of HYPNO are very promising with respect to other theorem provers for the same class of logics.

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PRONOM: Proof-Search and Countermodel Generation for Non-normal Modal Logics

Cited by 3 publications

References 19 publications

Countermodel Construction via Optimal Hypersequent Calculi for Non-normal Modal Logics

Countermodel Construction via Optimal Hypersequent Calculi for Non-normal Modal Logics

Proof-search and countermodel generation for non-normal modal logics: The theorem prover PRONOM

HYPNO: Theorem Proving with Hypersequent Calculi for Non-normal Modal Logics (System Description)

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