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This paper analyses the idea of strong equivalence for transition systems represented as logic programs under the Answer Set Programming (ASP) paradigm. To check strong equivalence, we use a linear temporal extension of Equilibrium Logic (a logical characterisation of ASP) and its monotonic basis, the intermediate logic of Here-and-There (HT). Trivially,… (More)

In this paper, we study a method for computing temporal equilibrium models, a generalisation of stable models for logic programs with temporal operators, as in Linear Temporal Logic (LTL). To this aim, we focus on a syntactic subclass of these temporal logic programs called splitable and whose main property is satisfying a kind of " future projected "… (More)

This paper contains a survey of the main definitions and results obtained up to date related to Temporal Equilibrium Logic, a non-monotonic hybrid approach that combines Equilibrium Logic (the best-known logical characterisation for the stable models semantics of logic programs) with Linear-Time Temporal Logic.

In this paper we consider the problem of introducing variables in temporal logic programs under the formalism of Temporal Equilibrium Logic (TEL), an extension of Answer Set Programming (ASP) for dealing with linear-time modal operators. We provide several fundamental contributions that pave the way for the implementation of a grounding process, that is, a… (More)

In this paper we provide an alternative semantics for Equilibrium Logic and its monotonic basis, the logic of Here-and-There (also known as Gödel's G3 logic) that relies on the idea of denotation of a formula, that is, a function that collects the set of models of that formula. Using the three-valued logic G3 as a starting point and an ordering relation… (More)

In this note we consider the problem of introducing variables in temporal logic programs under the formalism of Temporal Equilibrium Logic (TEL), an extension of Answer Set Programming (ASP) for dealing with linear-time modal operators. To this aim, we provide a definition of a first-order version of TEL that shares the syntax of first-order Linear-time… (More)

In this paper we present an extension of Peirce's existen-tial graphs to provide a diagrammatic representation of expressions in Quantified Equilibrium Logic (QEL). Using this formalisation, logical connectives are replaced by encircled regions (circles and squares) and quantified variables are represented as " identity " lines. Although the expressive… (More)

In this paper we study the relation between the two main extensions of Answer Set Programming with temporal modal operators: Temporal Equilibrium Logic (TEL) and Temporal Answer Sets (TAS). On the one hand, TEL is a complete non-monotonic logic that results from the combination of Linear-time Temporal Logic (LTL) with Equilibrium Logic. On the other hand,… (More)