The aim of this work is to develop a declarative semantics for N-Prolog with negation as failure. N-Prolog is an extension of Prolog proposed by Gabbay and Reyle, which allows for occurrences of nested implications in both goals and clauses. Our starting point is an operational semantics of the language defined by means of top-down derivation trees. Negation as finite failure can be naturally introduced in this context. A goal-G may be inferred from a database if every top-down derivation of (...) G from the database finitely fails, i.e., contains a failure node at finite height.Our purpose is to give a logical interpretation of the underlying operational semantics. In the present work we take into consideration only the basic problems of determining such an interpretation, so that our analysis will concentrate on the propositional case. Nevertheless we give an intuitive account of how to extend our results to a first order language. A full treatment of N-Prolog with quantifiers will be deferred to the second part of this work. (shrink)

We define a family of intuitionistic non-normal modal logics; they can be seen as intuitionistic counterparts of classical ones. We first consider monomodal logics, which contain only Necessity or Possibility. We then consider the more important case of bimodal logics, which contain both modal operators. In this case we define several interactions between Necessity and Possibility of increasing strength, although weaker than duality. We thereby obtain a lattice of 24 distinct bimodal logics. For all logics we provide both a Hilbert (...) axiomatisation and a cut-free sequent calculus, on its basis we also prove their decidability. We then define a semantic characterisation of our logics in terms of neighbourhood models containing two distinct neighbourhood functions corresponding to the two modalities. Our semantic framework captures modularly not only our systems but also already known intuitionistic non-normal modal logics such as Constructive K and the propositional fragment of Wijesekera’s Constructive Concurrent Dynamic Logic. (shrink)

Barlow's concept of the exploitation of environmental statistical regularities may be more plausibly related to brain mechanisms than Shepard's notion of internalisation. In our view, Barlow endorses a bottom-up approach to neural coding and processing, whereas we suggest that feedback interactions in the visual system, as well as chaotic correlation dynamics in the brain, are crucial in exploiting and assimilating environmental regularities. We also discuss the “conceptual tension” between Shepard's ideas of law internalisation and evolutionary adaptation. [Barlow; Shepard].

Fuzzy logics are many-valued logics that are well suited to reasoning in the context of vagueness. They provide the basis for the wider field of Fuzzy Logic, encompassing diverse areas such as fuzzy control, fuzzy databases, and fuzzy mathematics. This book provides an accessible and up-to-date introduction to this fast-growing and increasingly popular area. It focuses in particular on the development and applications of "proof-theoretic" presentations of fuzzy logics; the result of more than ten years of intensive work by researchers (...) in the area, including the authors. In addition to providing alternative elegant presentations of fuzzy logics, proof-theoretic methods are useful for addressing theoretical problems and developing efficient deduction and decision algorithms. Proof-theoretic presentations also place fuzzy logics in the broader landscape of non-classical logics, revealing deep relations with other logics studied in Computer Science, Mathematics, and Philosophy. The book builds methodically from the semantic origins of fuzzy logics to proof-theoretic presentations such as Hilbert and Gentzen systems, introducing both theoretical and practical applications of these presentations. (shrink)

Este trabajo iba a tratar sobre por qué el antropocentrismo es un problemairrelevante para las discusiones de bioética, y deberíamos prescindir de él.El argumento era que sostener una actitud antropocéntrica, tanto moderadacomo dura, tenía las mismas consecuencias a nivel práctico. Un antropocentristaapelará a la utilidad del medio ambiente y de las especies queen él habitan para la vida humana; y por ello sería importante que cuidaradel ecosistema para mantener dichos beneficios. Por otro lado un no-antropocentrista,apelará a que los animales y (...) el ecosistema cuentan con unasuerte de valor intrínseco y deberíamos cuidarlo apelando a dicho valor. Espor ello que las distinciones sólo podrían verse a un nivel teórico. (shrink)

Al principio este trabajo iba a tratar sobre por qué el antropocentrismo es un problema irrelevante para las discusiones de bioética y deberíamos prescindir de él. El argumento era que sostener una actitud antropocéntrica, tanto moderada como dura, tenía las mismas consecuencias a nivel práctico. Un antropocentrista apelará a la utilidad del medio ambiente y de las especies que en él habitan para la vida humana; y por ello sería importante que cuidara del ecosistema para mantener dichos beneficios. Por otro (...) lado, un no antropocentrista apelará a que los animales y el ecosistema cuentan con una suerte de valor intrínseco y deberíamos cuidarlos atendiendo a dicho valor. Es por ello que las distinciones sólo podrían verse a un nivel teórico. (shrink)

In this work we propose a labelled tableau method for Łukasiewicz infinite-valued logic Lω. The method is based on the Kripke semantics of this logic developed by Urquhart [25] and Scott [24]. On the one hand, our method falls under the general paradigm of labelled deduction [8] and it is rather close to the tableau systems for sub-structural logics proposed in [4]. On the other hand, it provides a CoNP decision procedure for Lω validity by reducing the check of branch (...) closure to linear programming. (shrink)

In this work we propose a labelled tableau method for ukasiewicz infinite-valued logic L . The method is based on the Kripke semantics of this logic developed by Urquhart [25] and Scott [24]. On the one hand, our method falls under the general paradigm of labelled deduction [8] and it is rather close to the tableau systems for sub-structural logics proposed in [4]. On the other hand, it provides a CoNP decision procedure for L validity by reducing the check of (...) branch closure to linear programming. (shrink)

Product logic Π is an important t-norm based fuzzy logic with conjunction interpreted as multiplication on the real unit interval [0,1], while Cancellative hoop logic CHL is a related logic with connectives interpreted as for Π but on the real unit interval with 0 removed (0,1]. Here we present several analytic proof systems for Π and CHL, including hypersequent calculi, co-NP labelled calculi and sequent calculi.

In this work we develop goal-directed deduction methods for the implicational fragment of several modal logics. We give sound and complete procedures for strict implication of K, T, K4, S4, K5, K45, KB, KTB, S5, G and for some intuitionistic variants. In order to achieve a uniform and concise presentation, we first develop our methods in the framework of Labelled Deductive Systems [Gabbay 96]. The proof systems we present are strongly analytical and satisfy a basic property of cut admissibility. We (...) then show that for most of the systems under consideration the labelling mechanism can be avoided by choosing an appropriate way of structuring theories. One peculiar feature of our proof systems is the use of restart rules which allow to re-ask the original goal of a deduction. In case of K, K4, S4 and G, we can eliminate such a rule, without loosing completeness. In all the other cases, by dropping such a rule, we get an intuitionistic variant of each system. The present results are part of a larger project of a goal directed proof theory for non-classical logics; the purpose of this project is to show that most implicational logics stem from slight variations of a unique deduction method, and from different ways of structuring theories. Moreover, the proof systems we present follow the logic programming style of deduction and seem promising for proof search [Gabbay and Reyle 84, Miller et al. 91]. (shrink)

The logic of Conditional Beliefs has been introduced by Board, Baltag, and Smets to reason about knowledge and revisable beliefs in a multi-agent setting. In this article both the semantics and the proof theory for this logic are studied. First, a natural semantics forCDLis defined in terms of neighbourhood models, a multi-agent generalisation of Lewis’ spheres models, and it is shown that the axiomatization ofCDLis sound and complete with respect to this semantics. Second, it is shown that the neighbourhood semantics (...) is equivalent to the original one defined in terms of plausibility models, by means of a direct correspondence between the two types of models. On the basis of neighbourhood semantics, a labelled sequent calculus forCDLis obtained. The calculus has strong proof-theoretic properties, in particular admissibility of contraction and cut, and it provides a decision procedure for the logic. Furthermore, its semantic completeness is used to obtain a constructive proof of the finite model property of the logic. Finally, it is shown that other doxastic operators can be easily captured within neighbourhood semantics. This fact provides further evidence of the naturalness of neighbourhood semantics for the analysis of epistemic/doxastic notions. (shrink)

Neuroimaging and psychophysiological techniques have proved to be useful in comprehending the extent to which the visual modality is pervasive in mental imagery, and in comprehending the specificity of images generated through other sensory modalities. Although further research is needed to understand the nature of mental images, data attained by means of these techniques suggest that mental imagery requires at least two distinct processing components.

In this paper we focus on theorem proving for conditional logics. First, we give a detailed description of CondLean, a theorem prover for some standard conditional logics. CondLean is a SICStus Prolog implementation of some labeled sequent calculi for conditional logics recently introduced. It is inspired to the so called “lean” methodology, even if it does not fit this style in a rigorous manner. CondLean also comprises a graphical interface written in Java. Furthermore, we introduce a goal-directed proof search mechanism, (...) derived from the above mentioned sequent calculi based on the notion of uniform proofs. Finally, we describe GOALDUCK, a simple SICStus Prolog implementation of the goal-directed calculus mentioned here above. Both the programs CondLean and GOALDUCK, together with their source code, are available for free download at. (shrink)

In dynamical systems models feedforward is needed to guide planning and to process unknown and unpredictable events. Feedforward could help Theory of Event Coding (TEC) integrate control processes and could model human performance in action planning in a more flexible and powerful way.

In diesem Beitrag möchte ich mich darauf beschränken, einige Aspekte von Fichtes Verhältnis zu Kant zu berücksichtigen, die mir sowohl für das Verständnis Fichtes als auch für das Verständnis Kants sehr lehrreich zu sein scheinen. Denn die Einsicht in die unterschiedlichen Auffassungen des alten und des jungen Denkers läßt um so mehr da, wo der zweite meint, den ersten bloß zu wiederholen, treu zu interpretieren oder allenfalls treu weiterzudenken, den Geist der beiden philosophischen Ansätze am deutlichsten zutage treten. Den manchmal (...) unbestimmten Ausdruck »Geist« darf man in diesem Fall wohl verwenden, da die Textstellen, die dem Vergleich feste Bezugspunkte angeben, nicht isoliert dastehen, sondern jeweils in zwei verschiedene und scharf konturierte philosophische Ansätze hinein konvergieren. (shrink)