Given a unimodal logic Λ extending the modal logic of reflexive frames T = K⊕2p→ p (the symbol ⊕ is used in the same way as in [3]), we can define several irreflexive or non-reflexive counterparts of Λ. Our first approach will be semantical. As usual, given a set W , define ∆W := {〈x, x〉 | x ∈W}. Definition 1.1 The irreflexivization of a frame F = 〈W,R〉 is 〈W,R〉• := 〈W,R − ∆W 〉. For X a class o...

This paper presents a fully abstract semantics for a variant of the untyped λ-calculus with recursive declarations. We first present a summary of existing work on full abstraction for the untyped λ-calculus, concentrating on ABRAMSKY and ONG’s work on the lazy λ-calculus. ABRAMSKY and ONG’s work is based on leftmost outermost reduction without sharing. This is notably inefficient, and many impl...

reversible logic circuits have found emerging attentions in nanotechnology,optical computing, quantum computing and low power design. a programmablelogic array (pla) is a universal circuit which is used to implement combinationallogic circuits. the main part of a pla is its and array. in this study we propose twotypes of optimized reversible programmable logic array (rpla) circuits. the firstty...

Relational semantics is one of the simplest and categorically most natural semantics of Linear Logic. The co-Kleisli category MRel associated with its multiset exponential comonad contains a fully abstract model of the untyped λ-calculus. That particular object of MRel is also a model of the resource λ-calculus, deriving from Ehrhard and Regnier’s differential extension of Linear Logic and rela...

Relational semantics for linear logic is a form of non-idempotent intersection type system, from which several informations on the execution of a proof-structure can be recovered. An element of the relational interpretation of a proof-structure R with conclusion Γ acts thus as a type (refining Γ) having R as an inhabitant. We are interested in the following type-checking question: given a proof...

3 Church’s simple theory of types (classical higher-order logic) 8 3.1 The λ-calculus as computation (middle and late 1930s) . . . . . . 8 3.2 Mixing λ-calculus and logic . . . . . . . . . . . . . . . . . . . . . 9 3.3 Simple types and typed λ-terms . . . . . . . . . . . . . . . . . . . 9 3.4 Formulas as terms of type o . . . . . . . . . . . . . . . . . . . . . 11 3.5 Elementary type theory . ....

A translation from higher-order logic (on top of the simply typed λ-calculus) to propositional logic is presented, such that the resulting propositional formula is satisfiable iff the HOL formula has a model of a given finite size. A standard SAT solver can then be used to search for a satisfying assignment, and such an assignment can be transformed back into a model for the HOL formula. The al...