A Tableau System for Right Propositional Neighborhood Logic over Finite Linear Orders: An Implementation

Bresolin, Davide; Monica, Dario Della; Montanari, Andrea; Sciavicco, Guido

doi:10.1007/978-3-642-40537-2_8

Cited by 3 publications

(2 citation statements)

References 12 publications

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“…Implemented decision procedures for interval temporal logics are not common in the literature. Among the few exceptions, a procedure for the fragment A of HS has been implemented in [BDMMS13,MMST14]; the former is an experimental implementation not aimed to computational efficiency, and the latter is an attempt to use an automatic tableaux generator, namely MetTeL 2 [TSK12]. The only previous attempt to apply a generic theorem prover to an interval temporal logic can be found in [BGMS10], where a tableau-based decision procedure for the fragment D, interpreted over dense linear orders, was developed in LoTREC [dCFG + 01].…”

Section: Resultsmentioning

confidence: 99%

On coarser interval temporal logics

Muñoz‐Velasco

Sala

Sciavicco

et al. 2019

Artificial Intelligence

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The primary characteristic of interval temporal logic is that intervals, rather than points, are taken as the primitive ontological entities. Given their generally bad computational behavior of interval temporal logics, several techniques exist to produce decidable and computationally affordable temporal logics based on intervals. In this paper we take inspiration from Golumbic and Shamir's coarser interval algebras, which generalize the classical Allen's Interval Algebra, in order to define two previously unknown variants of Halpern and Shoham's logic (HS) based on coarser relations. We prove that, perhaps surprisingly, the satisfiability problem for the coarsest of the two variants, namely HS 3 , not only is decidable, but PSpace-complete in the finite/discrete case, and PSpace-hard in any other case; besides proving its complexity bounds, we implement a tableau-based satisfiability checker for it and test it against a systematically generated benchmark. Our results are strengthened by showing that not all coarser-than-Allen's relations are a guarantee of decidability, as we prove that the second variant, namely HS 7 , remains undecidable in all interesting cases.

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Section: Resultsmentioning

confidence: 99%

On coarser interval temporal logics

Muñoz‐Velasco

Sala

Sciavicco

et al. 2019

Artificial Intelligence

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“…In contrast to non-modal characterisations of Allen's relations, pure modal varieties have so far had little practical take-up in applications in the targeted areas of Artificial Intelligence and Databases. Bresolin et al [5] seek to address this by presenting some early experience with a newly implemented decision procedure for one HS-sublogic (accessible online via [21]). Lomuscio and Michaliszyn [28] have been recently investigating extensions of HS-logic and associated algorithms intended for model checking multi-agent systems.…”

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confidence: 99%