The computer modelling of mathematical reasoning
The computer modelling of mathematical reasoning
Automated theorem-proving in non-classical logics
Automated theorem-proving in non-classical logics
A unified compilation style labelled deductive system for modal, substructural and fuzzy logics
Discovering the world with fuzzy logic
Symbolic Logic and Mechanical Theorem Proving
Symbolic Logic and Mechanical Theorem Proving
MGTP: A Model Generation Theorem Prover - Its Advanced Features and Applications
TABLEAUX '97 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
CLDS for Propositional Intuitionistic Logic
TABLEAUX '99 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
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The compilation approach for Labelled Deductive Systems (CLDS) is a general logical framework. Previously, it has been applied to various resource logics within natural deduction, tableaux and clausal systems, and in the latter case to yield a decidable (first order) CLDS for propositional Intuitionistic Logic (IL). In this paper the same clausal approach is used to obtain a decidable theorem prover for the implication fragments of propositional substructural Linear Logic (LL) and Relevance Logic (RL). The CLDS refutation method is based around a semantic approach using a translation technique utilising first-order logic together with a simple theorem prover for the translated theory using techniques drawn from Model Generation procedures. The resulting system is shown to correspond to a standard LL(RL) presentation as given by appropriate Hilbert axiom systems and to be decidable.