### Semantics Out of Context: Nominal Absolute Denotations for First-Order Logic and ComputationSemantics Out of Context: Nominal Absolute Denotations for First-Order Logic and Computation

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 Author Gabbay, Murdoch J. Source ACM Digital Library Content type Text Publisher Association for Computing Machinery (ACM) File Format PDF Copyright Year ©2016 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science Subject Keyword Nominal algebra ♦ Amgis-algebra ♦ First-order logic ♦ Fresh-finite limits ♦ Mathematical foundations ♦ Nominal lattices ♦ Semantics ♦ Sigma-algebra ♦ Variables Abstract Call a semantics for a language with variables $\textit{absolute}$ when variables map to fixed entities in the denotation. That is, a semantics is absolute when the denotation of a variable $\textit{a}$ is a copy of itself in the denotation. We give a trio of lattice-based, sets-based, and algebraic absolute semantics to first-order logic. Possibly open predicates are directly interpreted as lattice elements/sets/algebra elements, subject to suitable interpretations of the connectives and quantifiers. In particular, universal quantification $∀\textit{a}.&phis;$ is interpreted using a new notion of $\textit{“fresh-finite”}$ limit &bigwedge $^{#a}$ ⟦&phi⟧⟧ and using a novel dual to substitution. The interest in this semantics is partly in the nontrivial and beautiful technical details, which also offer certain advantages over existing semantics. Also, the fact that such semantics exist at all suggests a new way of looking at variables and the foundations of logic and computation, which may be well suited to the demands of modern computer science. ISSN 00045411 Age Range 18 to 22 years ♦ above 22 year Educational Use Research Education Level UG and PG Learning Resource Type Article Publisher Date 2016-06-01 Publisher Place New York e-ISSN 1557735X Journal Journal of the ACM (JACM) Volume Number 63 Issue Number 3 Page Count 66 Starting Page 1 Ending Page 66

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Source: ACM Digital Library