### A Normal Form for Linear Temporal Equilibrium Logic [chapter]

Pedro Cabalar
2010 Lecture Notes in Computer Science
In previous work, the so-called Temporal Equilibrium Logic (TEL) was introduced. This formalism provides an extension of the Answer Set semantics for logic programs to arbirary theories in the syntax of Linear Temporal Logic. It has been already shown that, in the nontemporal case, arbitrary propositional theories can always be reduced to logic program rules (with disjunction and negation in the head) independently on the context. That is, logic programs constitute a normal form for the
more » ... oral case. In this paper we show that TEL can be similarly reduced to a normal form consisting of a set of implications (embraced by a necessity operator) quite close to logic program rules. This normal form may be useful both for a practical implementation of TEL and a simpler analysis of theoretical problems. This research was partially supported by Spanish MEC project TIN2009-14562-C05-04 and Xunta de Galicia project INCITE08-PXIB105159PR. 1. M |= p if p ∈ H 0 , for any atom p. A theory is any set of formulas. An interpretation M is a model of a theory Γ , written M |= Γ , if M |= α, for all formula α ∈ Γ . We assume that a finite sequence M = m 1 , m 2 , . . . , m n is an abbreviation of an infinite sequence where the remaining elements coincide with m n , that is, that for i > n, m i = m n . The logic of THT is an orthogonal combination of