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1

On Modalities and Quantifiers

Fitting M.

Fundamenta Informaticae

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2017

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Vol. 156, nr 3/4

297--330

EN

In 1951 in his book An Essay in Modal Logic, Georg Henrik von Wright strongly called attention to the analogies between quantifiers and modal operators. In 1984 I published a paper in Synthese examining the analogy formally. Confession: the presentation in that paper was badly done, and there is a significant (though correctable) error. Its time to repair the damage, present the ideas in a better way, and continue the investigation further. There are natural sublogics of classical first-order logic that are direct analogs of standard, basic modal logics. The behavior of quantifiers can be given a possible world semantics, some analogous to normal models, some to regular models, and some to neighborhood models. The firstorder logics have axiom systems and generally also tableau systems, paralleling those of modal logics. Many have the interpolation property. This gives concrete substance to von Wright’s observations. But then, what is the crucial difference between modal operators and quantifiers? This turns out to be surprising in its simplicity, and leads to an interesting way of looking at the familiar Henkin style completeness proof for first-order logic.

2

A Tractable Rule Language in the Modal and Description Logic that Combines CPDL with Regular Grammar Logic

Nguyen L. A.

Fundamenta Informaticae

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2016

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Vol. 143, nr 1/2

113--139

EN

Combining CPDL (Propositional Dynamic Logic with Converse) and regular grammar logic results in an expressive modal logic denoted by CPDLreg. This logic covers TEAMLOG, a logical formalism used to express properties of agents’ cooperation in terms of beliefs, goals and intentions. It can also be used as a description logic for expressing terminological knowledge, in which both regular role inclusion axioms and CPDL-like role constructors are allowed. In this paper, we develop an expressive and tractable rule language called Horn-CPDLreg. As a special property, this rule language allows the concept constructor “universal restriction” to appear on the left hand side of general concept inclusion axioms. We use a special semantics for Horn-CPDLreg that is based on pseudo-interpretations. It is called the constructive semantics and coincides with the traditional semantics when the concept constructor “universal restriction” is disallowed on the left hand side of concept inclusion axioms or when the language is used as an epistemic formalism and the accessibility relations are serial. We provide an algorithm with PTIME data complexity for checking whether a knowledge base in Horn-CPDLreg has a pseudo-model. This shows that the instance checking problem in Horn-CPDLreg with respect to the constructive semantics has PTIME data complexity.

3

The contemporary concepts of development in terms of the diversifying criteria

Piontek Franciszek, Piontek Barbara

Problemy Ekorozwoju

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2014

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Vol. 9, nr 1

47--62

EN

In the 20th century, in the late 1990s and through the turn of the century, a lot of attention was paid to the so-called contemporary concepts of development. Simply speaking, it should be noted that those who discuss the concepts present their advantages and disadvantages, their common features, such as globality and a promise of happiness of the future generations, undefined in terms of time. The purpose of this paper is to analyze the so-called contemporary concept of development, in terms of the criteria that diversify them. We accept the following hypothesis for such a purpose: there are two subsets of the criteria diversifying the contemporary concepts of development: - the criteria of the philosophical nature, which diversify the development concepts ex ante: the relationship to existence and action, the relationship to axioms and natural law and to paradigms and the relationship to individual types of capital (economic, human and natural); - the criteria of the practical nature diversifying the contemporary concepts of development ex post, i.e. from the point of view of results in the real dimension: the relationship to consciousness, the relationship to the market, state and money, the relationship to technology, and the method of transforming contemporary global concepts into models of the local development. The paper gives the opportunity for further research, it presents issues, which should be a subject of multi-faceted analysis, and which include the basic issue: does the subject scope of a properly defined category of development include and can it accept the multitude of so-called concepts of development?

PL

W XX i na przełomie XXI wieku tak zwanym współczesnym koncepcjom rozwoju poświęca się wiele coraz więcej uwagi. Efektem tego są liczne opracowania poświęcone ich prezentacji. Zakres przedmiotowy tych opracowań obejmuje przede wszystkim przedmiot materialny głoszonych koncepcji: zagadnienie wzrostu gospodarczego, postępu technologicznego i cywilizacyjnego, przedstawienie zalet i wad, pozytywów i negatywów poszczególnych koncepcji rozwoju, ich wspólnych cech, jakimi są globalność i obiecywanie szczęścia przyszłych – bliżej w czasie nieokreślonych – pokoleń. Celem artykułu jest analiza tzw. współczesnych koncepcji rozwoju w aspekcie kryteriów, które je dywersyfikują. Tak sformułowany cel stanowi przedmiot niematerialny (formalny, zadany) dla podjętych w niniejszym artykule rozważań. Dla tak sformułowanego celu przyjmujemy następującą hipotezę: istnieją dwa podzbiory kryteriów dywersyfikujących współczesne koncepcje rozwoju: - kryteria o charakterze filozoficznym, które dywersyfikują koncepcje rozwoju ex ante: stosunek do istnienia i działania, stosunek do aksjomatów i prawa naturalnego a do paradygmatów i stosunek do poszczególnych kapitałów (ekonomiczny, ludzki i przyrodniczy); - kryteria o charakterze praktycznym dywersyfikujące współczesne koncepcje rozwoju ex post, czyli z punktu widzenia efektów w wymiarze realnym: stosunek do świadomości, stosunek do rynku, państwa i do pieniądza, stosunek do technologii, stosunek do efektywności oraz sposób transmisji współczesnych koncepcji globalnych do modeli rozwoju lokalnego. Artykuł prezentuje zagadnienia, które mogą i powinny stanowić wyzwanie do podejmowania dalszych badań i uwzględniać fundamentalną kwestię czy w zakresie przedmiotowym poprawnie zdefiniowanej kategorii rozwój mieści się i może być akceptowana wielość tak zwanych koncepcji rozwoju?