Sub-propositional Fragments of the Interval Temporal Logic of Allen’s Relations

Bresolin, Davide; Muñoz‐Velasco, Emilio; Sciavicco, Guido

doi:10.1007/978-3-319-11558-0_9

Cited by 11 publications

(14 citation statements)

References 18 publications

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“…We will describe the recently introduced sub-propositional fragments of HS [3,14,7,2]. First, we present the clausal form of HS-formulas.…”

Section: Language Modificationsmentioning

confidence: 99%

“…The aim of this paper is to investigate the expressive power of the temporal logic of Halpern and Shoham (HS in short) [1] and its sub-propositional fragments in which the use of propositional connectives is restricted [2,3,4]. These fragments are especially interesting due to a relatively low computational com-and computational complexity of these fragments have been intensively studied [2,5,6], their expressive power is yet to be studied in any significant depth. Our research aims at filling this gap.…”

Section: Introductionmentioning

confidence: 99%

“…Another method of restricting HS-formulas is based on their clausal representation [2]. The method is two folded: first, clauses are restricted to Horn form in which consequent of each clause consists of exactly one literal or core form in which both consequent and antecedent of each clause consists of exactly one literal.…”

Section: Introductionmentioning

confidence: 99%

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Hybrid fragments of Halpern–Shoham logic and their expressive power

Wałęga¹

2019

Theoretical Computer Science

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Halpern and Shoham modal logic of time intervals (HS in short) is an elegant and highly influential propositional interval-based modal logic. Its sub-propositional fragments, that is fragments obtained by restricting use of propositional connectives, and their hybrid extensions with nominals and satisfaction operators have been recently studied and successfully applied in real-world use cases. Detailed investigation of their decidability and computational complexity has been conducted, however, there has been significantly less research on their expressive power. In this paper we make a step towards filling this gap. In particular, we (1) compare classes of frames definable in full HS and in its hybrid extension, and (2) determine in which sub-propositional HS-fragments we can express the difference operator, nominals, and satisfaction operators. The obtained results enable us to classify HS, its sub-propositional fragments, and their hybrid extensions according to their expressive power.

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“…We will describe the recently introduced sub-propositional fragments of HS [3,14,7,2]. First, we present the clausal form of HS-formulas.…”

Section: Language Modificationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Hybrid fragments of Halpern–Shoham logic and their expressive power

Wałęga¹

2019

Theoretical Computer Science

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“…This method often results in fragments which have a good compromise between computational complexity and expressive power. Such fragments have been studied, e.g., in the case of linear temporal logic [1], temporal description logics [2], interval temporal logics [5,4], and, recently, normal modal logics K, T, K4, S4, and S5 [15,6]. Recall that K is the basic modal logic which semantically corresponds to the class of relational structures with an arbitrary binary relation, whereas in T, K4, S4, and S5 the relation is reflexive, transitive, a preorder (i.e., reflexive and transitive), and an equivalence, respectively.…”

Section: Introductionmentioning

confidence: 99%

Computational Complexity of Core Fragments of Modal Logics T, K4, and S4

Wałęga

2019

Logics in Artificial Intelligence

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“…The quest of computationally well-behaved restrictions of logics, and the observation that meaningful statements can be still expressed under sub-propositional restrictions has recently increased the interest in sub-propositional fragments of temporal description logics [AKRZ14], temporal logics [AKRZ13], and interval temporal logics [AKRZ15,BMS14]. However, sub-propositional modal logics have received little or no attention, with the exception of [CL94,FP87,Ngu04], which are limited to the Horn fragment.…”

Section: Introductionmentioning

confidence: 99%

On the Expressive Power of Sub-Propositional Fragments of Modal Logic

Bresolin

Muñoz‐Velasco

Sciavicco

2016

Electron. Proc. Theor. Comput. Sci.

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Modal logic is a paradigm for several useful and applicable formal systems in computer science. It generally retains the low complexity of classical propositional logic, but notable exceptions exist in the domains of description, temporal, and spatial logic, where the most expressive formalisms have a very high complexity or are even undecidable. In search of computationally well-behaved fragments, clausal forms and other sub-propositional restrictions of temporal and description logics have been recently studied. This renewed interest on sub-propositional logics, which mainly focus on the complexity of the various fragments, raise natural questions on their the relative expressive power, which we try to answer here for the basic multi-modal logic K N . We consider the Horn and the Krom restrictions, as well as the combined restriction (known as the core fragment) of modal logic, and, orthogonally, the fragments that emerge by disallowing boxes or diamonds from positive literals. We study the problem in a very general setting, to ease transferring our results to other meaningful cases.

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Sub-propositional Fragments of the Interval Temporal Logic of Allen’s Relations

Cited by 11 publications

References 18 publications

Hybrid fragments of Halpern–Shoham logic and their expressive power

Hybrid fragments of Halpern–Shoham logic and their expressive power

Computational Complexity of Core Fragments of Modal Logics T, K4, and S4

On the Expressive Power of Sub-Propositional Fragments of Modal Logic

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