On temporal logic versus datalog

Guessarian, Irène; Foustoucos, Eugenie; Andronikos, Theodore; Afrati, Foto N.

doi:10.1016/s0304-3975(02)00447-4

Cited by 3 publications

(13 citation statements)

References 32 publications

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“…programs corresponding to modal logic formulas). Even with this trivial bound, theorem 4 implies that the data complexity of stratified inf-Datalog is Ptime, hence adding greatest fixed points in a stratified way does not increase the evaluation complexity of Datalog (even though it increases its expressive power [16]).…”

Section: ⊓ ⊔mentioning

confidence: 99%

“…The basic definitions about Datalog can be found in [1,16,13], and the basic definitions about the µ-calculus and modal logic can be found in [3,9,10,19]. We proceed directly with the definition of inf-Datalog.…”

Section: Definitionsmentioning

confidence: 99%

“…In [16] we introduced the language inf-Datalog, which extends usual least fixpoint semantics of Datalog with greatest fixpoint semantics: greatest fixpoints are necessary for expressing properties such as fairness (something must happen infinitely often). Various temporal logics (CTL, ETL, alternation-free modal µ-calculus, and modal µ-calculus [9], by increasing order of expressive power) can be translated into Monadic inf-Datalog, and conversely fragments of Monadic inf-Datalog can be translated into these logics [16]. One of the advantages of inf-Datalog consists in eliminating problems inherent to negations: programs are assumed to be in positive normal form (negations affect only the explicitly given predicates); by duality, negation over computed predicates is expressed via greatest fixed points.…”

Section: Introductionmentioning

confidence: 99%

“…The data complexity is polynomialtime and linear-space. Using our succinct translations in [16] between the temporal logic paradigm and the database paradigm, we deduce upper bounds for the complexity of the model-checking problem for the modal µ-calculus.…”

Section: Introductionmentioning

confidence: 99%

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Inf-datalog, Modal Logic and Complexities

Foustoucos

Guessarian

2007

RAIRO-Theor. Inf. Appl.

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Inf-Datalog extends the usual least fixpoint semantics of Datalog with greatest fixpoint semantics: we defined inf-Datalog and characterized the expressive power of various fragments of inf-Datalog in [16]. In the present paper, we study the complexity of query evaluation on finite models for (various fragments of) inf-Datalog. We deduce a unified and elementary proof that global model-checking (computing all nodes satisfying a formula in a given structure) has 1. quadratic data complexity in time and linear program complexity in space for CT L and alternation-free modal µ-calculus, and 2. linear-space (data and program) complexities, linear-time program complexity and polynomial-time data complexity for Lµ k (modal µ-calculus with fixed alternation-depth at most k).

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Section: ⊓ ⊔mentioning

confidence: 99%

Section: Definitionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Inf-datalog, Modal Logic and Complexities

Foustoucos

Guessarian

2007

RAIRO-Theor. Inf. Appl.

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“…The successor predicate is needed to express the universal quantifier which in stratified Datalog can be captured by using the full power of negation. Note that we use the conventional semantics of Datalog and this constitutes a contribution relatively to previous works [GFAA03]. This is the third contribution.…”

Section: Introductionmentioning

confidence: 99%

From CTL to datalog

Afrati¹,

Andronikos²,

Pavlaki³

et al. 2003

Proceedings of the Paris C. Kanellakis Memorial Workshop on Principles of Computing &Amp; Knowledge: Paris C. Kanellakis Memori

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CTL is the dominant temporal specification language in practice mainly due to the fact that it admits model checking in linear time. Logic programming and the database query language Datalog are often used as an implementation platform for logic languages. In this paper we present the exact relation between CTL and Datalog and moreover we build on this relation and known efficient algorithms for CTL to obtain efficient algorithms for fragments of stratified Datalog. The contributions of this paper are: a) We embed CTL into STD which is a proper fragment of stratified Datalog. Moreover we show that STD expresses exactly CTLwe prove that by embedding STD into CTL. Both embeddings are linear. b) CTL can also be embedded to fragments of Datalog without negation. We define a fragment of Datalog with the successor build-in predicate that we call TDS and we embed CTL into TDS in linear time. We build on the above relations to answer open problems of stratified Datalog. We prove that query evaluation is linear and that containment and satisfiability problems are both decidable. The results presented in this paper are the first for fragments of stratified Datalog that are more general than those containing only unary EDBs. * The project is co -funded by the European Social Fund (75%) and National Resources (25%) -Operational Program for Educational and Vocational Training II (EPEAEK II) and particularly the Program HERAKLEITOS.

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Linear-Time Temporal Answer Set Programming

Aguado

Cabalar

Diéguez³

et al. 2021

Theory and Practice of Logic Programming

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In this survey, we present an overview on (Modal) Temporal Logic Programming in view of its application to Knowledge Representation and Declarative Problem Solving. The syntax of this extension of logic programs is the result of combining usual rules with temporal modal operators, as in Linear-time Temporal Logic (LTL). In the paper, we focus on the main recent results of the non-monotonic formalism called Temporal Equilibrium Logic (TEL) that is defined for the full syntax of LTL but involves a model selection criterion based on Equilibrium Logic, a well known logical characterization of Answer Set Programming (ASP). As a result, we obtain a proper extension of the stable models semantics for the general case of temporal formulas in the syntax of LTL. We recall the basic definitions for TEL and its monotonic basis, the temporal logic of Here-and-There (THT), and study the differences between finite and infinite trace length. We also provide further useful results, such as the translation into other formalisms like Quantified Equilibrium Logic and Second-order LTL, and some techniques for computing temporal stable models based on automata constructions. In the remainder of the paper, we focus on practical aspects, defining a syntactic fragment called (modal) temporal logic programs closer to ASP, and explaining how this has been exploited in the construction of the solver telingo, a temporal extension of the well-known ASP solver clingo that uses its incremental solving capabilities.

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On temporal logic versus datalog

Cited by 3 publications

References 32 publications

Inf-datalog, Modal Logic and Complexities

Inf-datalog, Modal Logic and Complexities

From CTL to datalog

Linear-Time Temporal Answer Set Programming

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