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1981•Notre Dame Journal of Formal LogicOpen access

A predicate logic based on indefinite description and two notions of identity.

Robert A. Alps, Robert C. Neveln

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Abstract

We present a formal 1 system of free predicate logic based on three primitives: indefinite description (using a variant of the Hubert 'e'-symbol) and two notions of identity, one reflexive and the other nonreflexive. This logic is intended to be of practical use in mathematics. Sample applications are given in Sections 13 and 16. We assume an axiomatic development of the usual sentence logic. For the predicate logic we list two primitive formulas

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We present a formal 1 system of free predicate logic based on three primitives: indefinite description (using a variant of the Hubert 'e'-symbol) and two notions of identity, one reflexive and the other nonreflexive. This logic is intended to be of practical use in mathematics. Sample applications are given in Sections 13 and 16. We assume an axiomatic development of the usual sentence logic. For the predicate logic we list two primitive formulas

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Available abstract

We present a formal 1 system of free predicate logic based on three primitives: indefinite description (using a variant of the Hubert 'e'-symbol) and two notions of identity, one reflexive and the other nonreflexive. This logic is intended to be of practical use in mathematics. Sample applications are given in Sections 13 and 16. We assume an axiomatic development of the usual sentence logic. For the predicate logic we list two primitive formulas

Key concepts: Predicate variable, Predicate functor logic, Predicate logic, Predicate (mathematical logic), Axiom, Higher-order logic, Mathematics, Predicate transformer semantics

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