Cut formulae and logic programming

In this paper we present a mechanism to define names for proof-witnesses of formulae and thus to use Gentzen's cut-rule in logic programming. We consider a program to be a set of logical formulae together with a list of such definitions. Occurrences of the defined names guide the proof-search by indicating when an instance of the cut-rule should be attempted. By using the cut-rule there are proofs that can be made dramatically shorter. We explain how this idea of using the cut-rule can be applied to the logic of hereditary Harrop formulae.Junta Nacional de Investigação Científica e Tecnológica (JNICT).União Europeia (UE) - Programa ESPRIT - grant BRA 7232 GENTZEN

Iluminando as mentes: da observação à disseminação dos fenómenos científicos

Este artigo faz uma breve contextualização de caráter historicista acerca da disseminação de conhecimento científico através dos instrumentos e aparelhos de visão. Localizamos o nascimento da ciência moderna no século XVII, época da Revolução Científica e do Iluminismo, responsáveis pela rutura com os paradigmas sociais, filosóficos, artísticos e científicos vigentes na época. No que diz respeito aos paradigmas científicos, tudo se funda numa nova atitude racionalista perante os fenómenos, acompanhada de uma metodologia e sistematização dos processos. Esta atitude passa sobretudo por um apuramento das técnicas de observação, beneficiadas pelos instrumentos, simultaneamente ferramentas e emblemas do ofício científico. Instrumentos de visão tal como o microscópio, o telescópio e os aparelhos fotográficos, que permitiram captar o infinitamente pequeno e o infinitamente grande, retratar o real e mais tarde estudar, documentar e reproduzir os fenómenos, exponenciando a disseminação do conhecimento científico, definindo também a ciência e as suas práticas

Proof search in constructive logics

We present an overview of some sequent calculi organised not for "theorem-proving" but for proof search, where the proofs themselves (and the avoidance of known proofs on backtracking) are objects of interest. The main calculus discussed is that of Herbelin [1994] for intuitionistic logic, which extends methods used in hereditary Harrop logic programming; we give a brief discussion of similar calculi for other logics. We also point out to some related work on permutations in intuitionistic Gentzen sequent calculi that clarifies the relationship between such calculi and natural deduction.Centro de Matemática da Universidade do Minho (CMAT).União Europeia (UE) - Programa ESPRIT - BRA 7232 Gentzen

Cut-elimination and a permutation-free sequent calculus for intuitionistic logic

We describe a sequent calculus, based on work of Herbelin's, of which the cut-free derivations are in 1-1 correspondence with normal natural deduction proofs of intuitionistic logic. We present a simple proof of Herbelin's strong cut-elimination theorem for the calculus, using the recursive path oredering theorem of Dershowitz.Junta Nacional de Investigação Científica e Tecnológica (JNICT).União Europeia (UE) - Programa ESPRIT - grant BRA 7232 GENTZEN

Proof search and counter-model construction for bi-intuitionistic propositional logic with labelled sequents

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. Negri's 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.Estonian Science Foundation - grants no. 5567; 6940Fundação para a Ciência e a Tecnologia (FCT)RESCUE - no. PTDC/EIA/65862/2006TYPES - FP6 ISTCentro de matemática da Universidade do Minh

Loop-free construction of counter-models for intuitionistic propositional logic

We present a non-looping method to construct Kripke trees refuting the non-theorems of intuitionistic propositional logic, using a contraction-free sequent calculus.União Europeia (UE) - project ESPRIT BRA 7232 GENTZEN.Junta Nacional de Investigação Científica e Tecnológica (JNICT)

Permutative conversions in intuitionistic multiary sequent calculi with cuts

This work presents an extension with cuts of Schwichtenberg's multiary sequent calculus. We identify a set of permutative conversions on it, prove their termination and confluence and establish the permutability theorem. We present our sequent calculus as the typing system of the {\em generalised multiary $\lambda$-calculus} lambda-Jm, a new calculus introduced in this work. Lambda-Jm corresponds to an extension of $\lambda$-calculus with a notion of {\em generalised multiary application}, which may be seen as a function applied to a list of arguments and then explicitly substituted in another term. Proof-theoretically the corresponding typing rule encompasses, in a modular way, generalised eliminations of von Plato and Herbelin's head cuts.Fundação para a Ciência e a Tecnologia (FCT)

A calculus of multiary sequent terms

Multiary sequent terms were originally introduced as a tool for proving termination of permutative conversions in cut-free sequent calculus. This work develops the language of multiary sequent terms into a term calculus for the computational (Curry-Howard) interpretation of a fragment of sequent calculus with cuts and cut-elimination rules. The system, named generalised multiary lambda-calculus, is a rich extension of the lambda-calculus where the computational content of the sequent calculus format is explained through an enlarged form of the application constructor. Such constructor exhibits the features of multiarity (the ability of forming lists of arguments) and generality (the ability of prescribing a kind of continuation). The system integrates in a modular way the multiary lambda-calculus and an isomorphic copy of the lambda-calculus with generalised application LambdaJ (in particular, natural deduction is captured internally up to isomorphism). In addition, the system: (i) comes with permutative conversion rules, whose role is to eliminate the new features of application; (ii) is equipped with reduction rules --- either the mu-rule, typical of the multiary setting, or rules for cut-elimination, which enlarge the ordinary beta-rule. This paper establishes the meta-theory of the system, with emphasis on the role of the mu-rule, and including a study of the interaction of reduction and permutative conversions.Fundação para a Ciência e a Tecnologia (FCT

Chitosan/alginate based multilayers to control drug release fromophthalmic lens

In this study we investigated the possibility of using layer-by-layer deposition, based in natural polymers (chitosan and alginate), to control the release of different ophthalmic drugs from three types of lens materials: a silicone-based hydrogel recently proposed by our group as drug releasing soft contact lens (SCL) material and two commercially available materials: CI26Y for intraocular lens (IOLs) and Definitive 50 for SCLs. The optimised coating, consisting in one double layer of (alginate – CaCl2)/(chitosan + glyoxal) topped with a final alginate-CaCl2 layer to avoid chitosan degradation by tear fluid proteins, proved to have excellent features to control the release of the anti-inflammatory, diclofenac, while keeping or improving the physical properties of the lenses. The coating leads to a controlled release of diclofenac from SCL and IOL materials for, at least, one week. Due to its high hydrophilicity (water contact angle ≈ 0) and biocompatibility, it should avoid the use of further surface treatments to enhance the useŕs comfort. However, the barrier effect of this coating is specific for diclofenac, giving evidence to the need of optimizing the chemical composition of the layers in view of the desired drug.info:eu-repo/semantics/publishedVersio

A Review of Heat Treatments on Improving the Quality and Residual Stresses of the Ti–6Al–4V Parts Produced by Additive Manufacturing

Additive manufacturing (AM) can be seen as a disruptive process that builds complex components layer upon layer. Two of its distinct technologies are Selective Laser Melting (SLM) and Electron Beam Melting (EBM), which are powder bed fusion processes that create metallic parts with the aid of a beam source. One of the most studied and manufactured superalloys in metal AM is the Ti–6Al–4V, which can be applied in the aerospace field due to its low density and high melting point, and in the biomedical area owing to its high corrosion resistance and excellent biocompatibility when in contact with tissues or bones of the human body. The research novelty of this work is the aggregation of all kinds of data from the last 20 years of investigation about Ti–6Al–4V parts manufactured via SLM and EBM, namely information related to residual stresses (RS), as well as the influence played by different heat treatments in reducing porosity and increasing mechanical properties. Throughout the report, it can be seen that the expected microstructure of the Ti–6Al–4V alloy is different in both manufacturing processes, mainly due to the distinct cooling rates. However, heat treatments can modify the microstructure, reduce RS, and increase the ductility, fatigue life, and hardness of the components. Furthermore, distinct post-treatments can induce compressive RS on the part’s surface, consequently enhancing the fatigue lifeinfo:eu-repo/semantics/publishedVersio