A Modal Logic for Quantification and Substitution
Copyright policy )A Modal Logic for Quantification and Substitution
Summary: The aim of this paper is to study the \(n\)-variable fragment of first order logic from a modal perspective. We define a modal formalism called cylindric mirror modal logic and show how it is a modal version of first order logic with substitution. In this approach, we can define a semantics for the language which is closely related to algebraic logic, as we find polyadic equality algebras as the modal or complex algebras of our system. The main contribution of the paper is a characterization of the intended `mirror cubic' frames of the formalisms and, a consequence of the special form of this characterization, a \ completeness theorem for these intended frames. As a consequence, we find complete finite yet unorthodox derivation systems for the equational theory of finite- dimensional representable polyadic equality algebras.
- Utrecht University Netherlands
logic with finitely many variables, polyadic equality algebras, cylindric mirror modal logic, equational theory, algebraic logic, \(n\)-variable fragment of first order logic, Wijsbegeerte, Cylindric and polyadic algebras; relation algebras, completeness, derivation rules, complex algebras, Nonclassical models (Boolean-valued, sheaf, etc.), Modal logic (including the logic of norms), Subsystems of classical logic (including intuitionistic logic), modal algebras, semantics, modal logic
logic with finitely many variables, polyadic equality algebras, cylindric mirror modal logic, equational theory, algebraic logic, \(n\)-variable fragment of first order logic, Wijsbegeerte, Cylindric and polyadic algebras; relation algebras, completeness, derivation rules, complex algebras, Nonclassical models (Boolean-valued, sheaf, etc.), Modal logic (including the logic of norms), Subsystems of classical logic (including intuitionistic logic), modal algebras, semantics, modal logic
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