A typed logic of partial functions reconstructed classically

Typed Norms for Typed Logic Programs

Curry-Typed Semantics in Typed Predicate Logic

Various questions arise in semantic analysis concerning the nature of types. These questions include whether we need types in a semantic theory, and if so, whether some version of simple type theory (STT, Church, 1940) is adequate or whether a richer more flexible theory is required to capture our semantic intuitions. Propositions and propositional attitudes can be represented in an essentially...

Partial Recursive Functions in Higher-Order Logic

Based on inductive definitions, we develop an automated tool for defining partial recursive functions in Higher-Order Logic and providing appropriate reasoning tools for them. Our method expresses termination in a uniform manner and includes a very general form of pattern matching, where patterns can be arbitrary expressions. Termination proofs can be deferred, restricted to subsets of argument...

Semantic Models for a Logic of Partial Functions

The Logic of Partial Functions (LPF) is used to reason about propositions that include terms that can fail to denote values. This paper provides semantics for LPF. A Structural Operational Semantics (SOS) provides an intuitive introduction; this is followed by a denotational semantics where the space of denotations is relations which provide an intuitive model of undefined terms. Finally, we il...

A Mechanization of Strong Kleene Logic for Partial Functions

Even though it is not very often admitted, partial functions do play a significant role in many practical applications of deduction systems. Kleene has already given a semantic account of partial functions using three-valued logic decades ago, but there has not been a satisfactory mechanization. Recent years have seen a thorough investigation of the framework of many-valued truth-functional log...