Semantically Constrained Condensed Detachment Is Incomplete Semantically Constrained Condensed Detachment Is Incomplete
نویسندگان
چکیده
In reporting on the theorem prover SCOTT (Slaney, SCOTT: A Semantically Guided Theorem Prover, Proc. IJCAI, 1993) we suggested semantic constraint as as an appropriate mechanism for guiding proof searches in propositional systems where the rule of inference is condensed detachment|a generalisation of Modus Ponens. Such constrained condensed detachment is closely analogous to semantic resolution. This paper exhibits an example which shows that semantically constrained condensed detachment is incomplete. That is, there are formulae deducible by means of condensed detachment which are not deducible when the semantic constraint is imposed. This answers an open question from our 1993 paper. Abstract In reporting on the theorem prover SCOTT (Slaney, SCOTT: A Semantically Guided Theorem Prover, Proc. IJCAI, 1993) we suggested semantic constraint as as an appropriate mechanism for guiding proof searches in propositional systems where the rule of inference is condensed detachment|a generalisation of Modus Ponens. Such constrained condensed detachment is closely analogous to semantic resolution. This paper exhibits an example which shows that semantically constrained condensed detachment is incomplete. That is, there are formulae de-ducible by means of condensed detachment which are not deducible when the semantic constraint is imposed. This answers an open question from our 1993 paper.
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