A general approach for determining the validity of commonsense assertions using conditional logics

✍ Scribed by Chris Groeneboer; James P. Delgrande

• Publisher: John Wiley and Sons
• Year: 1990
• Tongue: English
• Weight: 915 KB
• Volume: 5
• Category: Article
• ISSN: 0884-8173
• DOI: 10.1002/int.4550050505

✦ Synopsis

An approach to theorem proving for the class of normal conditional logics is presented. These logics have been shown to be appropriate for representing a wide variety of commonsense assertions, including default and prototypical properties, counterfactuals, notions of obligation, and others. The logics are based on a possible worlds semantics but unlike the better-known modal logics of necessity and possibility, they contain a binary "variable conditional" operator, 3, rather than a unary modal operator. The truth of a statement A j B depends both on the accessibility relation between worlds and on the propo:sition expressed by the antecedent A.

The approach develops an extension of the semantic tableaux approach to theorem proving. Basically, it consists in attempting to find an interpretation which will falsify a sentence or set of sentences. If successful, then a specific falsifying truth assignment is obtained; if not, then the sentence is valid. Since this method is based directly on the notion of truth, it is arguably more natural and intuitive than those based on prooftheoretic methods. The approach has been proven correct for the class of normal conditional logics. In addition, it has been implemented and tested on a number of different logics. Various heuristics have been incorporated, and the implementation, while exponential in the worst case, is shown to be reasonably efficient for a large set of test cases.