Fresh Logic: proof-theory and semantics for FM and nominal techniques
نویسنده
چکیده
In this paper we introduce Fresh Logic, a natural deduction style first-order logic extended with term-formers and quantifiers derived from the FM-sets model of names and binding in abstract syntax. Fresh Logic can be classical or intuitionistic depending on whether we include a law of excluded middle; we present a proof-normalisation procedure for the intuitionistic case and a semantics based on Kripke models in FM-sets for which it is sound and complete.
منابع مشابه
Modelling Generic Judgements
We propose a semantics for the ∇-quantifier of Miller and Tiu. First we consider the case for classical first-order logic. In this case, the interpretation is close to standard Tarski-semantics and completeness can be shown using a standard argument. Then we put our semantics into a broader context by giving a general interpretation of ∇ in categories with binding structure. Since categories wi...
متن کاملTruth Values and Connectives in Some Non-Classical Logics
The question as to whether the propositional logic of Heyting, which was a formalization of Brouwer's intuitionistic logic, is finitely many valued or not, was open for a while (the question was asked by Hahn). Kurt Gödel (1932) introduced an infinite decreasing chain of intermediate logics, which are known nowadays as Gödel logics, for showing that the intuitionistic logic is not finitely (man...
متن کاملNominal Algebra and the HSP Theorem
Nominal algebra is a logic of equality developed to reason algebraically in the presence of binding. In previous work it has been shown how nominal algebra can be used to specify and reason algebraically about systems with binding, such as first-order logic, the lambda-calculus, or process calculi. Nominal algebra has a semantics in nominal sets (sets with a finitely-supported permutation actio...
متن کاملNominal Logic: A First Order Theory of Names and Binding
This paper formalises within first-order logic some common practices in computer science to do with representing and reasoning about syntactical structures involving lexically scoped binding constructs. It introduces Nominal Logic, a version of first-order many-sorted logic with equality containing primitives for renaming via name-swapping, for freshness of names, and for name-binding. Its axio...
متن کاملThe Semantics of Nominal Logic Programs
Nominal logic programming is a form of logic programming with “concrete” names and binding, based on nominal logic, a theory of alpha-equivalence founded on swapping and freshness constraints. Previous papers have employed different characterizations of the semantics of nominal logic programs, including operational, denotational, and prooftheoretic characterizations. In this paper we give a uni...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- J. Applied Logic
دوره 5 شماره
صفحات -
تاریخ انتشار 2007