The universe of propositional approximations
The idea of approximate entailment has been proposed by Schaerf and Cadoli [Tractable reasoning via approximation, Artif. Intell. 74(2) (1995) 249-3 10] as a way of modelling the reasoning of an agent with limited resources. In that framework, a family of logics, parameterised by a set of propositional letters, approximates classical logic its the size of the set increases. The original proposal dealt only with formulas in clausal form, but in Finger and Wassermann [Approximate and limited reasoning: semantics, proof theory, expressivity and control, J. Logic Comput. 14(2) (2004) 179-204], one of the approximate systems was extended to deal with full propositional logic, giving the new system semantics, an axiomatisation, and a sound and complete proof method based on tableaux. In this paper, we extend another approximate system by Schaerf and Cadoli, presented in a subsequent work [M. Cadoli, M. Schaerf, The complexity of entailment in propositional multivalued logics, Ann. Math. Artif. Intell. 18(1) (1996) 29-50] and then take the idea further, presenting it more general approximation framework of which the previous ones are particular cases, and show how it can be used to formalise heuristics used in theorem proving, (c) 2006 Elsevier B.V. All rights reserved.
automated reasoning deductive systems approximate reasoning non-classical logics knowledge representation