v. 1. Úvod do filosofie. 1. Filosofická logika.

L’article esquisse d’abord le dispositif institutionnel d’accueil familial théra--peutique ( aft ) au sein duquel se déploie chez l’enfant la problématique étudiée – une affiliation spécifique en accueil familial. Il précise les conditions et les dynamiques de prise en charge en séparation protectrice, ici à dimension thérapeutique. Le cas clinique illustre l’évolution de l’affiliation, conforme à une longue expérience empirique acquise par l’équipe de professionnels dans l’accompagnent des dynamiques psychiques chez les enfants qui bénéficient de deux pôles d’affiliation, à travers (...) les liens avec la famille et la famille d’accueil. En appui sur les recherches et les articles parus sur ce sujet et sur les résultats d’une récente étude évoquant le destin des affiliations en accueil familial, l’auteur développe le concept de « double affiliation » que déploient les enfants en accueil familial dont le destin dépendra de la qualité du cadre d’accompagnement professionnel (humain et matériel) d’une telle situation existentielle extrême. (shrink)

Legitimate corporations exist within a common space that is shared with a different type of organization, one that is engaged in illicit or criminal activities.Activities taking place in this sector of the global commons threaten the integrity of the global markets and contribute to public distrust of corporations. In addition, they are placing legitimate organizations in an unanticipated and unwelcomed role within a larger law enforcement regime that requires them to participate in preventing the legitimization of illicit monetary gains through (...) money laundering. This paper provides information on the global initiatives implemented to curb money laundering. It concludes with a discussion of needed research. (shrink)

Facial perception plays a key role in various social interactions, including formidability assessments. People make relatively accurate inferences about men’s physical strength, aggressiveness, and success in physical confrontations based on facial cues. The physical factors related to the perception of fighting ability and their relative contribution have not been investigated yet, since most existing studies employed only a limited number of threat potential measures or proxies. In the present study, we collected data from Czech Mixed Martial Arts (MMA) fighters regarding (...) their fighting success and physical performance in order to test physical predictors of perceived fighting ability made on the basis of high-fidelity facial photographs. We have also explored the relationship between perceived and actual fighting ability. We created standardized 360° photographs of 44 MMA fighters which were assessed on their perceived fighting ability by 94 raters (46 males). Further, we obtained data regarding their physical characteristics (e.g. age, height, body composition) and performance (MMA score, isometric strength, anaerobic performance, lung capacity). In contrast to previous studies, we did not find any significant links between the actual and perceived fighting ability. The results of a multiple regression analysis have, however, shown that heavier fighters and those with higher anaerobic performance were judged as more successful. Our results suggest that certain physical performance-related characteristics are mirrored in individuals’ faces but assessments of fighting success based on facial cues are not congruent with actual fighting performance. (shrink)

Rational Pavelka logic extends Lukasiewicz infinitely valued logic by adding truth constants r̄ for rationals in [0, 1]. We show that this is a conservative extension. We note that this shows that provability degree can be defined in Lukasiewicz logic. We also give a counterexample to a soundness theorem of Belluce and Chang published in 1963.

Justification logics provide a framework for reasoning about justifications and evidence. In this article, we study a fuzzy variant of justification logics in which an agent’s justification for a belief has certainty degree between 0 and 1. We replace the classical base of justification logics with Hájek’s rational Pavelka logic. We introduce fuzzy possible world semantics with crisp accessibility relation and also single world models for our logics. We establish soundness and graded-style completeness for both kinds of semantics. We (...) also introduce extensions with product conjunction. Finally, we offer a solution to a variant of the sorites paradox in our fuzzy justification logics. (shrink)

Rational Pavelka logic extends Lukasiewicz infinitely valued logic $by adding truth constants \bar{r} for rationals in [0, 1].$ We show that this is a conservative extension. We note that this shows that provability degree can be defined in Lukasiewicz logic. We also give a counterexample to a soundness theorem of Belluce and Chang published in 1963.

An algebraic setting for the validity of Pavelka style completeness for some natural expansions of Łukasiewicz logic by new connectives and rational constants is given. This algebraic approach is based on the fact that the standard MV-algebra on the real segment [0, 1] is an injective MV-algebra. In particular the logics associated with MV-algebras with product and with divisible MV-algebras are considered.

In this paper we define the polyadic Pavelka algebras as algebraic structures for Rational Pavelka predicate calculus . We prove two representation theorems which are the algebraic counterpart of the completness theorem for RPL∀.

In this paper we prove polyadic counterparts of the Hájek, Paris and Shepherdson's conservative extension theorems of Łukasiewicz predicate logic to rational Pavelka predicate logic. We also discuss the algebraic correspondents of the provability and truth degree for polyadic MV-algebras and prove a representation theorem similar to the one for polyadic Pavelka algebras.

In [This Zeitschrift 25 , 45-52, 119-134, 447-464], Pavelka systematically discussed propositional calculi with values in enriched residuated lattices and developed a general framework for approximate reasoning. In the first part of this paper we introduce the concept of generalized quantifiers into Pavelka's logic and establish the fundamental theorem of ultraproduct in first order Pavelka's logic with generalized quantifiers. In the second part of this paper we show that the fundamental theorem of ultraproduct in first order (...) class='Hi'>Pavelka's logic is preserved under some direct product of lattices of truth values. (shrink)

We consider first-order infinite-valued Łukasiewicz logic and its expansion, first-order rational Pavelka logic RPL∀. From the viewpoint of provability, we compare several Gentzen-type hypersequent calculi for these logics with each other and with Hájek’s Hilbert-type calculi for the same logics. To facilitate comparing previously known calculi for the logics, we define two new analytic calculi for RPL∀ and include them in our comparison. The key part of the comparison is a density elimination proof that introduces no cuts for one (...) of the hypersequent calculi considered. (shrink)

The paper deals with fuzzy Horn logic which is a fragment of predicate fuzzy logic with evaluated syntax. Formulas of FHL are of the form of simple implications between identities. We show that one can have Pavelka-style completeness of FHL w.r.t. semantics over the unit interval [0, 1] with left-continuous t-norm and a residuated implication, provided that only certain fuzzy sets of formulas are considered. The model classes of fuzzy structures of FHL are characterized by closure properties. We also (...) give comments on related topics proposed by N. Weaver. (shrink)

This paper presents a logical Style painting classifier based on evaluated Horn clauses, qualitative colour descriptors and Explanations. Three versions of $\ell $-SHE are defined, using rational Pavelka logic, and expansions of Gödel logic and product logic with rational constants: RPL, $G$ and $\sqcap $, respectively. We introduce a fuzzy representation of the more representative colour traits for the Baroque, the Impressionism and the Post-Impressionism art styles. The $\ell $-SHE algorithm has been implemented in Swi-Prolog and tested on 90 (...) paintings of the QArt-Dataset and on 247 paintings of the Paintings-91-PIB dataset. The percentages of accuracy obtained in the QArt-Dataset for each $\ell $-SHE version are 73.3%, 65.6% $) and 68.9% $). Regarding the Paintings-91-PIB dataset, the percentages of accuracy obtained for each $\ell $-SHE version are 60.2%, 48.2% $) and 57.0% $). Our logic definition for the Baroque style has obtained the highest accuracy in both datasets, for all the $\ell $-SHE versions. An important feature of the classifier is that it provides reasons regarding why a painting belongs to a certain style. The classifier also provides reasons about why outliers of one art style may belong to another art style, giving a second classification option depending on its membership degrees to these styles. (shrink)

We introduce a propositional many-valued modal logic which is an extension of the Continuous Propositional Logic to a modal system. Otherwise said, we extend the minimal modal logic to a Continuous Logic system. After introducing semantics, axioms and deduction rules, we establish some preliminary results. Then we prove the equivalence between consistency and satisfiability. As straightforward consequences, we get compactness, an approximated completeness theorem, in the vein of Continuous Logic, and a Pavelka-style completeness theorem.

Presented is a completeness theorem for fuzzy equational logic with truth values in a complete residuated lattice: Given a fuzzy set Σ of identities and an identity p≈q, the degree to which p≈q syntactically follows (is provable) from Σ equals the degree to which p≈q semantically follows from Σ. Pavelka style generalization of well-known Birkhoff's theorem is therefore established.

Many results in fuzzy logic depend on the mathematical structure the truth value set obeys. In this textbook the algebraic foundations of many-valued and fuzzy reasoning are introduced. The book is self-contained, thus no previous knowledge in algebra or in logic is required. It contains 134 exercises with complete answers, and can therefore be used as teaching material at universities for both undergraduated and post-graduated courses. Chapter 1 starts from such basic concepts as order, lattice, equivalence and residuated lattice. It (...) contains a full section on BL-algebras. Chapter 2 concerns MV-algebra and its basic properties. Chapter 3 applies these mathematical results on Lukasiewicz-Pavelka style fuzzy logic, which is studied in details; besides semantics, syntax and completeness of this logic, a lot of examples are given. Chapter 4 shows the connection between fuzzy relations, approximate reasoning and fuzzy IF-THEN rules to residuated lattices. (shrink)

The paper presents generalizations of results on so-called Horn logic, well-known in universal algebra, to the setting of fuzzy logic. The theories we consider consist of formulas which are implications between identities (equations) with premises weighted by truth degrees. We adopt Pavelka style: theories are fuzzy sets of formulas and we consider degrees of provability of formulas from theories. Our basic structure of truth degrees is a complete residuated lattice. We derive a Pavelka-style completeness theorem (degree of provability (...) equals degree of truth) from which we get some particular cases by imposing restrictions on the formulas under consideration. As a particular case, we obtain completeness of fuzzy equational logic. (shrink)

In this paper we provide a finite axiomatization (using two finitary rules only) for the propositional logic (called $L\Pi$ ) resulting from the combination of Lukasiewicz and Product Logics, together with the logic obtained by from $L \Pi$ by the adding of a constant symbol and of a defining axiom for $\frac{1}{2}$ , called $L \Pi\frac{1}{2}$ . We show that $L \Pi \frac{1}{2}$ contains all the most important propositional fuzzy logics: Lukasiewicz Logic, Product Logic, Gödel's Fuzzy Logic, Takeuti and Titani's (...) Propositional Logic, Pavelka's Rational Logic, Pavelka's Rational Product Logic, the Lukasiewicz Logic with $\Delta$ , and the Product and Gödel's Logics with $\Delta$ and involution. Standard completeness results are proved by means of investigating the algebras corresponding to $L \Pi$ and $L \Pi \frac{1}{2}$ . For these algebras, we prove a theorem of subdirect representation and we show that linearly ordered algebras can be represented as algebras on the unit interval of either a linearly ordered field, or of the ordered ring of integers, Z. (shrink)

ABSTRACT The term fuzzy logic has two different meanings -broad and narrow. In Zadeh's opinion, fuzzy logic is an extension of many- valued logic but having a different agenda—as generalized modus ponens, max-min inference, linguistic quantifiers etc. The question we address in this paper is whether there is something in Zadeh's specific agenda which cannot be grasped by “classiceli”, “traditional” mathematical logic. We show that much of fuzzy logic can be understood as classical deduction in a many-sorted many-valued Pavelka- (...) Lukasiewicz style rational quantification logic. This means that, besides the linguistic or approximation aspects, the logical aspect is present too and can be made explicit. (shrink)

A many-valued sentential logic with truth values in an injective MV-algebra is introduced and the axiomatizability of this logic is proved. The paper develops some ideas of Goguen and generalizes the results of Pavelka on the unit interval. The proof for completeness is purely algebraic. A corollary of the Completeness Theorem is that fuzzy logic on the unit interval is semantically complete if and only if the algebra of the truth values is a complete MV-algebra. In the well-defined fuzzy (...) sentential logic holds the Compactness Theorem, while the Deduction Theorem and the Finiteness Theorem in general do not hold. Because of its generality and good-behaviour, MV-valued logic can be regarded as a mathematical basis of fuzzy reasoning. (shrink)

In this paper, we introduce a foundation for computable model theory of rational Pavelka logic and continuous logic, and prove effective versions of some related theorems in model theory. We show how to reduce continuous logic to rational Pavelka logic. We also define notions of computability and decidability of a model for logics with computable, but uncountable, set of truth values; we show that provability degree of a formula with respect to a linear theory is computable, and use (...) this to carry out an effective Henkin construction. Therefore, for any effectively given consistent linear theory in continuous logic, we effectively produce its decidable model. This is the best possible, since we show that the computable model theory of continuous logic is an extension of computable model theory of classical logic. We conclude with noting that the unique separable model of a separably categorical and computably axiomatizable theory is decidable. (shrink)

We present logic programming style “goal-directed” proof methods for Łukasiewicz logic Ł that both have a logical interpretation, and provide a suitable basis for implementation. We introduce a basic version, similar to goal-directed calculi for other logics, and make refinements to improve efficiency and obtain termination. We then provide an algorithm for fuzzy logic programming in Rational Pavelka logic RPL, an extension of Ł with rational constants.

The logics RŁ, RP, and RG have been obtained by expanding Łukasiewicz logic Ł, product logic P, and Gödel–Dummett logic G with rational constants. We study the lattices of extensions and structural completeness of these three expansions, obtaining results that stand in contrast to the known situation in Ł, P, and G. Namely, RŁ is hereditarily structurally complete. RP is algebraized by the variety of rational product algebras that we show to be Q-universal. We provide a base of admissible rules (...) in RP, show their decidability, and characterize passive structural completeness for extensions of RP. Furthermore, structural completeness, hereditary structural completeness, and active structural completeness coincide for extensions of RP, and this is also the case for extensions of RG, where in turn passive structural completeness is characterized by the equivalent algebraic semantics having the joint embedding property. For nontrivial axiomatic extensions of RG, we provide a base of admissible rules. We leave the problem open whether the variety of rational Gödel algebras is Q-universal. (shrink)