Temporal Here and There

Temporal Here and There (THT) constitutes the logical foundations of Temporal Equilibrium Logic. Nevertheless, it has never been studied in detail since results about axiomatisation and interdefinability of modal operators remained unknown. In this paper we provide a sound and complete axiomatic system for THT together with several results on interdefinability of modal operators.

[1]  David Pearce,et al.  A Characterization of Strong Equivalence for Logic Programs with Variables , 2007, LPNMR.

[2]  Pedro Cabalar,et al.  Strong Equivalence of Non-Monotonic Temporal Theories , 2014, KR.

[3]  Pedro Cabalar,et al.  Propositional theories are strongly equivalent to logic programs , 2007, Theory Pract. Log. Program..

[4]  Luis Fariñas del Cerro,et al.  Epistemic Equilibrium Logic , 2015, IJCAI.

[5]  Yuri Gureoich Intuitionistic Logic , 2008 .

[6]  David Pearce,et al.  Quantified Equilibrium Logic and Foundations for Answer Set Programs , 2008, ICLP.

[7]  R. Goldblatt Logics of Time and Computation , 1987 .

[8]  Pedro Cabalar,et al.  An infinitary encoding of temporal equilibrium logic* , 2015, Theory and Practice of Logic Programming.

[9]  Ilkka Niemelä,et al.  Logic programs with stable model semantics as a constraint programming paradigm , 1999, Annals of Mathematics and Artificial Intelligence.

[10]  M. de Rijke,et al.  Bisimulations for Temporal Logic , 1997, J. Log. Lang. Inf..

[11]  A. Heyting Die formalen Regeln der intuitionistischen Logik , 1930 .

[12]  Dirk van Dalen,et al.  Logic and structure , 1980 .

[13]  Victor W. Marek,et al.  Stable models and an alternative logic programming paradigm , 1998, The Logic Programming Paradigm.

[14]  Fred Kröger,et al.  Temporal Logic of Programs , 1987, EATCS Monographs on Theoretical Computer Science.

[15]  David Pearce,et al.  A denotational semantics for equilibrium logic* , 2015, Theory and Practice of Logic Programming.

[16]  Pedro Cabalar,et al.  Temporal Equilibrium Logic: A First Approach , 2007, EUROCAST.

[17]  Alex K. Simpson,et al.  The proof theory and semantics of intuitionistic modal logic , 1994 .

[18]  Johan Anthory Willem Kamp,et al.  Tense logic and the theory of linear order , 1968 .

[19]  David Pearce,et al.  Equilibrium logic , 2006, Annals of Mathematics and Artificial Intelligence.