The universe of propositional approximations

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Abstract

The idea of approximate entailment has been proposed by Schaerf and Cadoli [Tractable reasoning via approximation, Artif. Intell. 74(2) (1995) 249–310] 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 as 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 a 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.

Keywords

Automated reasoning
Deductive systems
Approximate reasoning
Non-classical logics
Knowledge representation

Cited by (0)

1

Partly supported by the Brazilian Research Council (CNPq), Grant PQ 300597/95-5.

2

Partly supported by CNPq Grant PQ 300196/01-6.