Luís F. Pinto

Type-based termination of recursive definitions

This paper introduces

Permutability of proofs in intuitionistic sequent calculi

\lambda^\widehat

Proof Search and Counter-Model Construction for Bi-intuitionistic Propositional Logic with Labelled Sequents

, a simply typed lambda calculus supporting inductive types and recursive function definitions with termination ensured by types. The system is shown to enjoy subject reduction, strong normalisation of typable terms and to be stronger than a related system

Model checking embedded systems with PROMELA

\lambda_{\mathcal{G}}

Relating sequent calculi for bi-intuitionistic propositional logic

in which termination is ensured by a syntactic guard condition. The system can, at will, be extended to support coinductive types and corecursive function definitions also.

Confluence and Strong Normalisation of the Generalised Multiary λ-Calculus

Abstract We prove a folklore theorem, that two derivations in a cut-free sequent calculus for intuitionistic propositional logic (based on Kleenes G3) are inter-permutable (using a set of basic “permutation reduction rules” derived from Kleenes work in 1952) iff they determine the same natural deduction. The basic rules form a confluent and weakly normalising rewriting system. We refer to Schwichtenbergs proof elsewhere that a modification of this system is strongly normalising.

Monadic translation of classical sequent calculus

Bi-intuitionistic logic is a conservative extension of intuitionistic logic with a connective dual to implication, called exclusion. We present a sound and complete cut-free labelled sequent calculus for bi-intuitionistic propositional logic, BiInt, following S. Negris general method for devising sequent calculi for normal modal logics. Although it arises as a natural formalization of the Kripke semantics, it is does not directly support proof search. To describe a proof search procedure, we develop a more algorithmic version that also allows for counter-model extraction from a failed proof attempt.

Sequent Calculi for the Normal Terms of the λΠ- and λΠ∑-Calculi

The design process for embedded systems can benefit from the usage of formal methods, if some properties of the systems are checked, before design and implementation decisions are accomplished. This paper presents a model checking approach using the Spin tool, to verify some important properties of embedded systems, namely liveness, deadlock-freedom, and structural conflicts among transitions. The systems are modelled with a variant of Petri nets, called SIPN (synchronous and interpreted Petri nets), and this paper discusses how SIPN models should be specified with the PROMELA language (input format for the Spin model checker). The approach is exemplified with a case study.

A proof-theoretic study of bi-intuitionistic propositional sequent calculus

Bi-intuitionistic logic is the conservative extension of i ntuitionistic logic with a connective dual to implication. It is sometimes presented as a symmetric constructive subsystem of classical logic. In this paper, we compare three sequent calculi for bi-intui tionistic propositional logic: (1) a basic standard-style sequent calculus that restricts the pre mises of implication-right and exclusion-left inferences to be single-conclusion resp. single-assumpti on and is incomplete without the cut rule, (2) ? (( ??

A calculus of multiary sequent terms

In a previous work we introduced the generalised multiaryλ-calculus λ J m , an extension of the λ-calculus where functions can be applied to lists of arguments (a feature which we call “multiarity”) and encompassing “generalised” eliminations of von Plato. In this paper we prove confluence and strong normalisation of the reduction relations of λ J m . Proofs of these results lift corresponding ones obtained by Joachimski and Matthes for the system Λ J. Such lifting requires the study of how multiarity and some forms of generality can express each other. This study identifies a variant of λJ, and another system isomorphic to it, as being the subsystems of λ J m with, respectively, minimal and maximal use of multiarity. We argue then that λ J m is the system with the right use of multiarity.