Logic Functors: A Toolbox of Components for Building Customized and Embeddable Logics
Résumé
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).