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Introduction to Logic, 2nd Edition by Eric Kao, Michael Genesereth

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CHAPTER 7

Relational Logic Proofs

7.1 INTRODUCTION

Logical entailment for Relational Logic is defined the same as for Propositional Logic. A set of premises logically entails a conclusion if and only if every truth assignment that satisfies the premises also satisfies the conclusions. In the case of Propositional Logic, we can check logical entailment by examining a truth table for the language. With finitely many proposition constants, the truth table is large but finite. For Relational Logic, things are not so easy. It is possible to have Herbrand bases of infinite size; and, in such cases, truth assignments are infinitely large and there are infinitely many of them, making it impossible to check logical entailment using truth tables.

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