A Logic-Based Calculus of Fluents

This report formally defines the class of all problems on {\em Reasoning about Actions and Change}, where accurate and complete information about actions, together with strict inertia in continuous time, continuous change and alternative results of possibly concurrent and independent actions are the assumed properties. The intended model set for each member in the class is defined in terms of a model-theoretic trajectory semantics. The case is designated, in the {\em Features and Fluents} framework, with the~\KRACi family of reasoning problems. A fix-point characterization of the subclass \KspRAdCi is then given in terms of a simulative algebraic semantics, and show which are the difficulties when approaching the full class with that method. A non-simulative algebraic semantics is then presented as an alternative algebraic characterization of the model-theoretic trajectory semantics. Still the characterization is made in terms of complete lattices and continuous operators on those complete lattices. The algebraic semantics is shown to be correct and complete with respect to the trajectory-semantics, when applied to reasoning problems in \KRACi. Finally, adopting the non-simulative algebraic semantics as proof procedure, a logic-based {\em Calculus~of~Fluents} is defined, via a meta-theoretic extension of the Horn Clause Logic using the non-ground representation of object level variables. The meta-interpreter consists in the Horn clause representation of the proof procedure. The calculus is shown to be decidable, domain independent and class dependent; its semantics consists in the non-simulative algebraic semantics, and is executable as a logic program by the SLD-resolution rule.