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# Logic Functors: A Toolbox of Components for Building Customized and Embeddable Logics

1 Lande - Logiciel : ANalyse et DEveloppement
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, Inria Rennes – Bretagne Atlantique
Abstract : Logic Functors form a framework for specifying new logics, and deriving automatically theorem provers and consistency/completeness diagnoses. Atomic functors are logics for manipulating symbols and concrete domains, while other functors are logic transformers that may add connectives or recursive structures, or may alter the semantics of a logic. The semantic structure of the framework is model theoretic as opposed to the verifunctional style often used in classical logic. This comes close to the semantics of description logics, and we show indeed that the logic $\calALC$ can be rebuilt using logic functors. This offers the immediate advantage that variants of $\calALC$ can be explored and implemented almost for free. This report comes with extensive appendices describing in detail a toolbox of logic functors (definitions, algorithms, theorems, and proofs).
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Reports (Research report)
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https://hal.inria.fr/inria-00070155
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Submitted on : Friday, May 19, 2006 - 7:16:38 PM
Last modification on : Wednesday, October 26, 2022 - 8:16:25 AM
Long-term archiving on: : Sunday, April 4, 2010 - 8:20:11 PM

### Identifiers

• HAL Id : inria-00070155, version 1

### Citation

Sébastien Ferré, Olivier Ridoux. Logic Functors: A Toolbox of Components for Building Customized and Embeddable Logics. [Research Report] RR-5871, INRIA. 2006, pp.103. ⟨inria-00070155⟩

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