Hedges and successors in basic algebras

The concept of hedge was introduced by Zadeh in the sake to amplify true values of linguistic terms. It was used by Bělohlávek and Vychodil for formal concept analysis of unsharp reasoning. The concept of successor was introduced by Caicedo and Cignoli for study of intuitionistic connectives and used by San Martín, Castiglioni, Menni and Sagastume in Heyting algebras. Since basic algebras form an algebraic tool for simultaneous treaty of many-valued logics and logics of quantum mechanics, it arises a natural question of generalization of these concepts also for basic algebras. This motivated our investigations on hedges and successors.     

Computer science and the market: Metamorphoses of fundamental ideas

Conclusion The interest in open systems in the West is increasing year after year. CSCW is thus slanted to become the most popular scientific-technical direction of the first years of the next century, especially as a result of the increased activity of American providers and the U.S. government program for the creation of an Internet-based “information highway of the century” [14]. For instance, as part of the program for large-scale acceptance of Internet, the U.S. National Science Foundation (NSF) allocates funding only to organizations that make their projects available on Internet [15], and the European Community officially subjected all European research to specific networking requirements [16]. Theoretical topics of CSCW, including computer hermeneutics and development of “computer Esperanto” will thus be strongly influenced by information science and information infrastructure, which are changing the industry of information production and information use in “first world” countries. We hope that we have managed to demonstrate that the drama in computer science is an apparent phenomenon, which is attributable in our domestic conditions to the absence of direct and effective links with the “open world”. Our view can be supported by the thought expressed by A. Toffler: “…some scientists paint a picture of the world of science as activated by its own inner logic and evolving according to its own laws in total isolation of the surrounding world. In this connection we cannot but remark that scientific hypotheses, theories, metaphors, and models are formed under the influence of economic, cultural, and political factors acting outside the walls of laboratories” [17]. If the forms of cognitive practice change with changes in methods of production, forms of social organization, engineering and technology, this means that we must elucidate the relationship between cognition and action, between theoretical and applied practice, between consciousness and behavior…. Where scientific research goes into decline, we observe narrow specialization of the scientific language and loss of its connections with the daily language.M. Wartofsky,Models Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 112–124, March–April, 1995.     

Some results on the Collatz problem

The paper refers to the Collatz's conjecture. In the first part, we present some equivalent forms of this conjecture and a slight generalization of a former result from [1]. Then, we present the notion of “chain subtrees” in Collatz's tree followed by a characterization theorem and some subclass of numbers which are labels for some chain subtrees. Next, we define the notion of “fixed points” and using this, we give another conjecture similar to Collatz's conjecture. Some new infinite sets of numbers for which the Collatz's conjecture holds are given. Finally, we present some interesting results related to the number of “even” and “odd” branches in the Collatz's tree. Received: 15 September 1999 / 2 June 2000     

On very true operators on pocrims

Hájek introduced the logic enriching the logic BL by a unary connective vt which is a formalization of Zadeh’s fuzzy truth value “very true”. algebras, i.e., BL-algebras with unary operations, called vt-operators, which are among others subdiagonal, are an algebraic counterpart of Partially ordered commutative integral residuated monoids (pocrims) are common generalizations of both BL-algebras and Heyting algebras. The aim of our paper is to introduce and study algebraic properties of pocrims endowed by “very-true” and “very-false”-like operators. Research is supported by the Research and Development Council of Czech Government via project MSN 6198959214.     

Logical approximation II

 The paper continues a study of extensional formulas and their representation by normal forms. The notion of extensional formula is extended to the case when extensionality is considered with respect to a binary reflexive relation. It has been proved that extensional formulas can be represented by normal forms of infinite type and “approximated” by normal forms of finite type. All proofs are given formally in fuzzy predicate BL-logic.     

Tensor products of MV-algebras

 The structure of MV-module over a PMV-algebra was defined in [5]. In this paper we test this notion in the important problem of scalar extension. The tensor product ⊗ _mv defined in [11] is generalized and another tensor product, ⊗ _o , is studied in relation with the corresponding tensor product of ℓ-groups [9]. Using tensor products we get the free MV-modules over a totally ordered PMV-algebra. Dedicated to Prof. Ján Jakubíik on the occasion of his 80th birthday     

Some principles of coordinated decision making in distributed systems

Conclusion The proposed approach leads to flexible decision support algorithms and procedures that easily adapt to changing requirements. The application of the proposed principles is illustrated in [12] with the object of allowing for the specific features of the problem and accelerating convergence of distributed decision support systems. The application of these principles to the construction of various control procedures and decision support scheme is demonstrated in [13–19]. At the present time, in connection with active transition to the market and operation in a rapidly changing reality, we can expect an increase in demand for algorithms, procedures, and schemes that divide the domains of competence, sharply delineate the domains of responsibility, and clearly separate the fields of action of the “center” and the “periphery” [11]. The need for such procedures will also be felt in financial management support [26–27] and in macro/micro economic modeling and forecasting [20–26]. This is due to the fact that in our rapidly changing world we are often unable to identify several separate criteria for optimization. We are often forced to look for a decision which is admissible by a whole range of formal and informal criteria and is stable under small perturbations of both the criteria and the external conditions [28–30]. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 161–175, March–April, 1996.     

Conceptual characteristic features of fault-free hardware design

We consider the concept of active diagnostics for detecting and registering hardware faults in computers, sensors, executive mechanisms, and optical electronic systems. We propose a collection of informative features to detect and register sources of the faults: connectors, contacting units of large integral circuits (LIC) and super-large integral circuits (SLIC), contacting conductors on printed circuit boards (including multilayered ones), interface buses, unshielded single- and multicore wires, grounding and power buses, connector blocks, brazing joints. Based on these new properties of passive elements in radioelectronic hardware, and in keeping with the notion of “fail-safeness,” we propose a new notion of reliability, “fault-safeness,” that establishes a connection between hardware faults and its hidden defects.     

Unfolding San Lorenzo

This paper proposes a “reading” of the church of San Lorenzo in Turin, designed by Guarino Guarini, through the philosophical notion of “fold” introduced by Gilles Deleuze. The paper consists of two parts. The first part contains an exploration of the notion of “fold” in architecture and in philosophy and examines the use of the fold in the theory of Baroque architecture as well as the range of this new tool in architectural practise in contemporary architecture and in philosophy and examines the use of the fold as fundamental condition for understanding Baroque era. The second part contains the application of the notion of fold as a philosophical and conceptual framework for the “reading” of the chapel.     

Hyper-Contradictions, Generalized Truth Values and Logics of Truth and Falsehood

In Philosophical Logic, the Liar Paradox has been used to motivate the introduction of both truth value gaps and truth value gluts. Moreover, in the light of “revenge Liar” arguments, also higher-order combinations of generalized truth values have been suggested to account for so-called hyper-contradictions. In the present paper, Graham Priest's treatment of generalized truth values is scrutinized and compared with another strategy of generalizing the set of classical truth values and defining an entailment relation on the resulting sets of higher-order values. This method is based on the concept of a multilattice. If the method is applied to the set of truth values of Belnap's “useful four-valued logic”, one obtains a trilattice, and, more generally, structures here called Belnap-trilattices. As in Priest's case, it is shown that the generalized truth values motivated by hyper-contradictions have no effect on the logic. Whereas Priest's construction in terms of designated truth values always results in his Logic of Paradox, the present construction in terms of truth and falsity orderings always results in First Degree Entailment. However, it is observed that applying the multilattice-approach to Priest's initial set of truth values leads to an interesting algebraic structure of a “bi-and-a-half” lattice which determines seven-valued logics different from Priest's Logic of Paradox.     

Gradual elements in a fuzzy set

The notion of a fuzzy set stems from considering sets where, in the words of Zadeh, the “transition from non-membership to membership is gradual rather than abrupt”. This paper introduces a new concept in fuzzy set theory, that of a gradual element. It embodies the idea of fuzziness only, thus contributing to the distinction between fuzziness and imprecision. A gradual element is to an element of a set what a fuzzy set is to a set. A gradual element is as precise as an element, but the former is flexible while the latter is fixed. The gradual nature of an element may express the idea that the choice of this element depends on a parameter expressing some relevance or describing some concept. Applications of this notion to fuzzy cardinality, fuzzy interval analysis, fuzzy optimization, and defuzzification principles are outlined.     

System design of “Ba”-like stages for improvisational acts via Leibnizian space–time and Peirce’s existential graph concepts

A framework for “improvisational” social acts and communication is introduced by referring to the idea of “relationalism” such as natural farming, permaculture and deep ecology. Based on this conception, the notion of Existential Graph by C. S. Peirce is introduced. The notion of extended self in deep ecology is substantiated based on the Roy Adaptation Model in Nursing Theory and Narrative approaches. By focusing on Leibnizian notions of space and time and by introducing Petri net, a spatio-temporal model of improvisation is constructed. This model is expected to substantiate the interesting notion of “Ba” proposed by H. Shimizu reflecting Japanese culture.     

An anytime revision operator for large and uncertain geographic data sets

 The environmental data are in general imprecise and uncertain, but they are located in space and therefore obey to spatial constraints. The “spatial analysis” is a (natural) reasoning process through which geographers take advantage of these constraints to reduce this uncertainty and to improve their beliefs. Trying to automate this process is a really hard problem. We propose here the design of a revision operator able to perform a spatial analysis in the context of one particular “application profile”: it identifies objects bearing a same variable bound through local constraints. The formal background, on which this operator is built, is a decision algorithm from Reiter [9]; then the heuristics, which help this algorithm to become tractable on a true scale application, are special patterns for clauses and “spatial confinement” of conflicts. This operator is “anytime”, because it uses “samples” and works on small (tractable) blocks, it reaggregates the partial revision results on larger blocks, thus we name it a “hierarchical block revision” operator. Finally we illustrate a particular application: a flooding propagation. Of course this is among possible approaches of “soft-computing” for geographic applications. On leave at: Centre de Recherche en Géomatique Pavillon Casault, Université Laval Québec, Qc, Canada – G1K 7P4 Université de Toulon et du Var, Avenue de l'Université, BP 132, 83957 La Garde Cedex, France This work is currently supported by the European Community under the IST-1999-14189 project.     

Fast access to concepts in concept lattices via bidirectional associative memories

Bidirectional associative memories (BAMs) are shown to be capable of precisely learning concept lattice structures by Radim Belohlávek. The focus of this letter is to show that the BAM, when set up with a concept lattice by setting up connection weights according to the rule proposed by Belohlávek, always returns the most specific or most generic concept containing the given set of objects or attributes when a set of objects or attributes is presented as input to the object or attribute layer. A proof of this property is given here, together with an example, and a brief application of the property is provided.     

Passive-state generation mechanisms and stabilization of dynamic systems

Conclusion In the models of passive-state formation considered above we have assumed for simplicity constant control parameters. In reality, the control parameters are functions of time, environmental factors, and the values of the “active” variables [7, 8]. These functions are “reasonably” constructed: under “bad” conditions the variables shift to a passive state, and when “good” conditions are restored, the variables switch back to active state. It is relevant to develop and analyze the corresponding model circuits. Here we can expect to observe even stronger stabilization effects in the behavior of complex systems. In conclusion, I would like to thank an anonymous referee for useful comments. The study is financed by the Russian Foundation of Basic Research. Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 103–112, November–December, 1995.     

Matters of (Meta-) Modeling

With the recent trend to model driven engineering a common understanding of basic notions such as “model” and “metamodel” becomes a pivotal issue. Even though these notions have been in widespread use for quite a while, there is still little consensus about when exactly it is appropriate to use them. The aim of this article is to start establishing a consensus about generally acceptable terminology. Its main contributions are the distinction between two fundamentally different kinds of model roles, i.e. “token model” versus “type model” (The terms “type” and “token” have been introduced by C.S. Peirce, 1839–1914.), a formal notion of “metaness”, and the consideration of “generalization” as yet another basic relationship between models. In particular, the recognition of the fundamental difference between the above mentioned two kinds of model roles is crucial in order to enable communication among the model driven engineering community that is free of both unnoticed misunderstandings and unnecessary disagreement.     

Crypt-equivalent algebraic specifications

Summary Equivalence is a fundamental notion for the semantic analysis of algebraic specifications. In this paper the notion of “crypt-equivalence” is introduced and studied w.r.t. two “loose” approaches to the semantics of an algebraic specificationT: the class of all first-order models ofT and the class of all term-generated models ofT. Two specifications are called crypt-equivalent if for one specification there exists a predicate logic formula which implicitly defines an expansion (by new functions) of every model of that specification in such a way that the expansion (after forgetting unnecessary functions) is homologous to a model of the other specification, and if vice versa there exists another predicate logic formula with the same properties for the other specification. We speak of “first-order crypt-equivalence” if this holds for all first-order models, and of “inductive crypt-equivalence” if this holds for all term-generated models. Characterizations and structural properties of these notions are studied. In particular, it is shown that firstorder crypt-equivalence is equivalent to the existence of explicit definitions and that in case of “positive definability” two first-order crypt-equivalent specifications admit the same categories of models and homomorphisms. Similarly, two specifications which are inductively crypt-equivalent via sufficiently complete implicit definitions determine the same associated categories. Moreover, crypt-equivalence is compared with other notions of equivalence for algebraic specifications: in particular, it is shown that first-order cryptequivalence is strictly coarser than “abstract semantic equivalence” and that inductive crypt-equivalence is strictly finer than “inductive simulation equivalence” and “implementation equivalence”.     

Probabilistic asynchronous automata

Asynchronous automata were introduced by W. Zielonka as an algebraic model of distributed systems, showing that the class of trace languages recognizable by automata over free partially commutative monoids coincides with the class of trace languages recognizable by deterministic asynchronous automata. In this paper we extend the notion of asynchronous automata to the probabilistic case. Our main result is a nontrivial generalization to Zielonka's theorem: we prove that the sets of behaviors of probabilistic automata and of probabilistic asynchronous automata coincide in the case of concurrent alphabets with acyclic dependency graphs. This research has been supported by European Projects EBRA Nos. 3148 (DEMON), 3166 (ASMICS), and 6317 (ASMICS2), by MURST 40%, and by the CNR Project “Modelli di Computazione Parallela.”     

Locally strong coherence and inference with lower–upper probabilities

 We introduce an operational way to reduce the spatial complexity in inference processes based on conditional lower–upper probabilities assessments. To reach such goal we must suitably exploit zero probabilities taking account of logical conditions characterizing locally strong coherence. We actually re-formulate for conditional lower–upper probabilities the notion of locally strong coherence already introduced for conditional precise probabilities. Thanks to the characterization, we avoid to build all atoms, so that several real problems become feasible. In fact, the real complexity problem is connected to the number of atoms. Since for an inferential process with lower–upper probabilities several sequences of constraints must be fulfilled, our simplification can have either a “global” or a “partial” effect, being applicable to all or just to some sequences. The whole procedure has been implemented by XLisp-Stat language. A comparison with other approaches will be done by an example. The contribution of L. Galli has been essentially addressed to some aspects of the algorithm's implementation.     

On BCK algebras: Part II: New algebras. The ordinal sum (product) of two bounded BCK algebras

Since all the algebras connected to logic have, more or less explicitly, an associated order relation, it follows, by duality principle, that they have two presentations, dual to each other. We classify these dual presentations in “left” and “right” ones and we consider that, when dealing with several algebras in the same research, it is useful to present them unitarily, either as “left” algebras or as “right” algebras. In some circumstances, this choice is essential, for instance if we want to build the ordinal sum (product) between a BL algebra and an MV algebra. We have chosen the “left” presentation and several algebras of logic have been redefined as particular cases of BCK algebras. We introduce several new properties of algebras of logic, besides those usually existing in the literature, which generate a more refined classification, depending on the properties satisfied. In this work (Parts I–V) we make an exhaustive study of these algebras—with two bounds and with one bound—and we present classes of finite examples, in bounded case. In Part II, we continue to present new properties, and consequently new algebras; among them, bounded α γ algebra is a common generalization of MTL algebra and divisible bounded residuated lattice (bounded commutative Rl-monoid). We introduce and study the ordinal sum (product) of two bounded BCK algebras. Dedicated to Grigore C. Moisil (1906–1973).