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20 Causal and Probabilistic Reasoning in Plog

In this paper we give an overview of the knowledge representation (KR) language Plog [Baral, Gelfond, and Rushton 2009] whose design was greatly influenced by work of Judea Pearl. We introduce the syntax and semantics of P-log, give a number of examples of its use for knowledge representation, and discuss the role Pearl’s ideas played in the design of the language. Most of the technical material presented in the paper is not new. There are however two novel technical contributions which could be of interest. First we expand P-log semantics to allow domains with infinite Herbrand bases. This allows us to represent infinite sequences of random variables and (indirectly) continuous random variables. Second we generalize the logical base of P-log which improves the degree of elaboration tolerance of the language. The goal of the P-log designers was to create a KR-language allowing natural and elaboration tolerant representation of commonsense knowledge involving logic and probabilities. The logical framework of P-log is Answer Set Prolog (ASP) — a language for knowledge representation and reasoning based on the answer set semantics (aka stable model semantics) of logic programs [Gelfond and Lifschitz 1988; Gelfond and Lifschitz 1991]. ASP has roots in declarative programing, the syntax and semantics of standard Prolog, disjunctive databases, and non-monotonic logic. The semantics of ASP captures the notion of possible beliefs of a reasoner who adheres to the rationality principle which says that “One shall not believe anything one is not forced to believe”. The entailment relation of ASP is non-monotonic, which facilitates a high degree of elaboration tolerance in ASP theories. ASP allows natural representation of defaults and their exceptions, causal relations (including effects of actions), agents’ intentions and obligations, and other constructs of natural language. ASP has a number of efficient reasoning systems, a well developed mathematical theory, and a well tested methodology of representing and using knowledge for computational tasks (see, for instance, [Baral 2003]). This, together with the fact that some of the designers of P-log came from the ASP community made the choice of a logical foundation for P-log comparatively easy.