The aim of this paper is to discuss the design of an explicitly typed λ-calculus corresponding to the Intersection Type Assignment System (IT ), which assigns intersection types to the untyped λ-calculus. Two different proposals are given. The logical foundation of all of them is the Intersection Logic IL.

The λ-calculus is destructive: its main computational mechanism – beta reduction – destroys the redex and makes it thus impossible to replay the computational steps. Combinatory logic is a variant of the λ-calculus which maintains irreversibility. Recently, reversible computational models have been studied mainly in the context of quantum computation, as (without measurements) quantum physics i...

We introduce refutationally complete superposition calculi for intentional and extensional λ-free higher-order logic, a formalism that allows partial application and applied variables. The intentional variants perfectly coincide with standard superposition on first-order clauses. The calculi are parameterized by a well-founded term order that need not be compatible with arguments, making it pos...

Combinatory logic shows that bound variables can be eliminated without loss of expressiveness. It has applications both in the foundations of mathematics and in the implementation of functional programming languages. The original combinatory calculus corresponds to minimal implicative logic written in a system “à la Hilbert”. We present in this paper a combinatory logic which corresponds to pro...

The aim of this paper is to discuss the design of an explicitly typed λ-calculus corresponding to the Intersection Type Assignment System (IT ), which assigns intersection types to the untyped λ-calculus. Two different proposals are given. The logical foundation of all of them is the Intersection Logic IL.

Quality of Service (QoS) refers to a set of rules or techniques that help the network administrators use the available network resources optimally to manage the effects of congestion and to treat the applications according to their needs. The differentiated services architecture (DiffServ) allows providing quality of service to users. The major DiffServ premise is that individual flows with sim...

We translate the argumentation networks A = (S,R) into a theory ∆A of intuitionistic logic, retaining S as the domain and using intuitionistic negation to model the attack R in A: the attack xRy is translated to x → ¬y. The intuitionistic models of ∆A characterise the complete extensions of A. The reduction of argumentation networks to intuitionistic logic yields, in addition to a representatio...

We extend Ehrhard Regnier's di erential linear logic along the lines of Laurent's polarization. We provide a denotational semantics of this new system in the well-known relational model of linear logic, extending canonically the semantics of both di erential and polarized linear logics: this justi es our choice of cut elimination rules. Then we show this polarized di erential linear logic re ne...

quality of service (qos) refers to a set of rules or techniques that help the network administrators use the available network resources optimally to manage the effects of congestion and to treat the applications according to their needs. the differentiated services architecture (diffserv) allows providing quality of service to users. the major diffserv premise is that individual flows with sim...

We discuss a ‘negative’ way of defining frame classes in (multi-)modal logic, and address the question whether these classes can be axiomatized by derivation rules, the ‘non-ξ rules’, styled after Gabbay’s Irreflexivity Rule. The main result of this paper is a meta-theorem on completeness, of the following kind: If Λ is a derivation system having a set of axioms that are special Sahlqvist formu...