We have given a framework that provides uniform and modular presentations and implementations of families of non-classical logics in terms of labelled deduction systems: logics in a family are presented as extensions of a fixed base system, consisting of rules for local and non-local operators, with theories comprised of (Horn) rules formalizing the properties of the relations connecting worlds in the underlying Kripkestyle semantics and, in the case of quantified logics, the way domains of individuals change between worlds. The previous chapters demonstrate, we think, that our systems fit well into the Logical Framework setting (our Isabelle encodings provide a simple and natural environment for interactive proof development that supports hierarchical structuring), and have modular metatheoretical properties, in particular soundness and completeness, and normalization of derivations and a subformula property, which we can exploit to delineate advantages and limitations of our approach.1
KeywordsModal Logic Deduction System Predicate Logic Natural Deduction Automate Theorem Prove
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