Counterfactuals, cotenability and consistency

Abstract

This paper describes the formal basis for the implementation of counterfactual queries in the experimental CLOGPROG (‘Conditional Logic Programming’) system. In particular, we concentrate on counterfactuals based on a relevant logic, although much of the work is applicable to non-relevant systems. Besides nested conditionals, the language of the system extends PROLOG by allowing negation in assertion positions; this is not negation-as-failure, but a form of inconsistency tolerating ‘DeMorgan’ negation. We show how the counterfactual discussion can be simply extended to provide a means of enforcing consistency with respect to this negation. We sketch the details of the computational model implemented in CLOGPROG; this is an incomplete, but stable and well-behaved approximation to the full theoretical treatment. To focus attention on the special issues of counterfactuals, we restrict ourselves here to the propositional part of the system.