Argument Calculus and Networks

A major reason behind the success of prob­ ability calculus is that it possesses an um­ ber of valuable tools, which are based on the notion of probabilistic indepen­ dence. In this paper, I identify a no­ tion of logical independence that makes some of these tools available to a class of propositional databases, called argument databases. Specifi cally, I suggest a graph­ ical representation of argument databases, called argument networks, which resemble Bayesian networks. I also suggest an al­ gorithm for reasoning with argument net­ works, which resembles a basic algorithm for reasoning with Bayesian networks. Fi­ nally, I show that argument networks have several applications: Nonmonotonic rea­ soning, truth maintenance, and diagnosis. A major reason behind the success of probability cal­ culus is that it possesses a number of valuable tools, which are based on the notion of probabilistic inde­ pendence [Pearl, 1988]. In this paper, I identify an intuitive notion of logical independence that makes some of these tools available to a special class of propositional databases. In particular, I identify in Section 2 a class of propo­ sitional databases, called argument databases, and study some of their properties. In Section 3, I iden­ tify a notion of logical independence with respect to argument databases and study its properties. In Sec­ tion 4, I suggest a graphical representation of argu­ ment databases, called argument networks, which re­ semble Bayesian networks. And in Section 5, I sug­ gest an algorithm for reasoning with argument net­ works, which resembles a basic algorithm for reason­ ing with Bayesian networks. Finally, I show in Sec­ tion 6 that argument networks have several applica­ tions: Nonmonotonic reasoning, truth maintenance, and diagnosis. Proofs, omitted due to space limita­ tions, can be found in the full version of this paper. 2 ARGUMENT DATABASES Logical independence, to be defined in Section 3, is based on three notions: argument databases, argu­ ments, and conditional arguments, which are counter­ parts of probability distributions, probabilities, and conditional probabilities. This section explores these three notions in some detail. Definition 1 Let .C and A be two propositional languages over disjoint primitive propositions. An argument database d with respect to (.C, A) is a set of sentences a ::::> ¢>, where sentence a belongs to language A, sentence <P belongs to language C, and database d does not entail any invalid sentence in language A.1 Example 1 Let .C be …