
Authors:
Janusz CIUCIURA
Title:Negations in the Adjunctive Discursive Logic
Pages:143160
File:bibtex
Abstract ( + )
In the logical literature, Discursive (or Discussive) Logic introduced by Stanislaw Jaskowski is seen as one of the earliest examples of the socalled paraconsistent logic. Nevertheless, there is some confusion over what discursive logic actually is. One of the possible sources of the confusion may be easily discerned; it comes from the fact that Jaskowski published his two papers in Polish and their English translations appeared many years later. Up till 1999, no one but a Polish reader was able to read Jaskowski`s paper on the discursive conjunction and, consequently some authors took discursive logic to be a foremost example of a nonadjunctive logic.
The situation became even more complicated when da Costa, Dubikajtis and Kotas presented an axiomatization with discursive connectives as primitive symbols. It turned out that a connective of the discursive conjunction they considered did not correspond to any of Jaskowski`s connectives. Thus, their axiomatization contained some axiom schemata that were not generally valid in Jaskowski`s logic.
The purpose of this paper is to clarify the confusion surrounding the discursive logic. We will present a direct semantics and axiomatization of Jaskowski`s adjunctive discursive logic and show how to define and axiomatize two additional connectives of negation.

Authors:
Szymon FRANKOWSKI
Title:Plausible Reasoning Expressed by pConsequence
Pages:161170
File:bibtex
Abstract ( + )
In this paper we describe a formal way of describing of plausible (or nondeductive) reasoning. Ajdukiewicz's distinction between deductive an nondeductive reasoning is our theoretical framework. In this paper we present a formal way of describing plausible (or nondeductive) reasoning. Ajdukiewicz's distinction between deductive and nondeductive reasoning [1] provides our theoretical framework. Our formal approach is given by so called operation of pconsequence, which has been described earlier e.g. in [2]. At every stage of our work we try to show that Ajdukiewicz's framework is relevant for our investigations. In the last paragraph axiomatization of "plausible" counterpart of Lukasiewicz's many valued logics is given.

Authors:
Andrzej INDRZEJCZAK
Title:Correspondence Theory in Proof
Pages:171183
File:bibtex
Abstract ( + )
Correspondence (or definability) theory is one of the most important ingredients of the theory of modal logics developed in the last three decades. Generality of its results is in striking contrast to the situation in proof theory. The latter suffers from the lack of general solutions not only for modal logics but for nonclassical logics in general. On the other hand, a lot of case studies devoted to the investigations on relations between particular formalizations of particular classes of logics is enormous and still growing. It seems that some synthesis of various results can improve the situation and provide a firm basis for the development of a theory being a counterpart of semantical correspondence theory.
The following considerations have preliminary character and provide nothing more than an incomplete list of some proposals and future expectations. However, the reader should remember that it is a text on something that, in fact, does not exist, but written in the belief that it might and should do.

Authors:
Krystyna MRUCZEKNASIENIEWSKA, Marek NASIENIEWSKI
Title:Paraconsitent Logics Obtained by J.Y.Beziau's Method by Means of some NonNormal Modal Logics
Pages:185196
File:bibtex
Abstract ( + )
The paper presents a formulation of some propositional logics. J.Y.Beziau formulated a logic called Z. The present paper is a contribution to a further generalization for those frames in which nonnormal worlds are allowed.

Authors:
Marek NASIENIEWSKI, Andrzej PIETRUSZCZAK
Title:The Weakest Regular Modal Logic Defining Jaskowski's Logic D2
Pages:197210
File:bibtex
Abstract ( + )
Jaskowski's logic D2 was formulated with the help of the modal logic S5. It was shown that to define D2 one could use normal modal logics weaker than S5. In the present paper we indicate a certain regular modal logic which also defines D2. This logic is the weakest regular modal logic defining D2.

Authors:
Maciej NOWICKI
Title:QLRegular Quantified Modal Logics
Pages:211221
File:bibtex
Abstract ( + )
We show completeness for firstorder counterparts of Lemmon's modal propositional logics C1, D1 and E1 examined by Andrzej Pietruszczak.

Authors:
Tomasz JARMUZEK
Title:Tableau System for Logic of Categorial Propositions and Decidability
Pages:223231
File:bibtex
Abstract ( + )
n the article we present an application of some tableaux method. It is used to define a certain system of syllogistic. We consider only the basic system with Aristotelian sentences but without the assumption on nonemptiness. The presented approach can be effectively extended to enriched syllogistic in some of many ways. However, here we limit ourselves to the most basic and general perspective. Thanks to it and the method we use, we can consider a problem of decidability. Since we consider a pure syllogistic language, without boolean connectives, so we come to slightly different results. At the end we show a very simple connection between the formal structures of reasoning and a cardinality of domain, which is sufficient to decide whether a given reasoning is valid or not.

Authors:
Janusz KACZMAREK
Title:What is a Formalized Ontology Today? An Example of IIC
Pages:233244
File:bibtex
Abstract ( + )
The paper presents some proposal of formalized ontology. It is based on Meinongian ideas (complete and incomplete objects), as well as formally given structures of individuals, kinds and concepts. These structures are used, in the next step, to construct semantics for modal logic S4 thus yielding ontological version of it, i.e. OS4. Some selected theorems of proposed ontology referring to ontological objects are given.

Authors:
Grzegorz MALINOWSKI
Title:Fregean Axiom and ManyValuedness
Pages:245252
File:bibtex
Abstract ( + )
The Fregean Axiom, FA is an assumption that logical values and denotations of sentences are the same in number. Since the set of logical values consists of two elements: the true and the false, FA reduces the set of possible denotations of sentences to two, as well.
We aim at applying more logical values within the original Fregean Scheme. The proposal may ultimately be related to any finite number of values. However, in the present paper we will concentrate on the case of threeelement set of values only. The most important reason for doing so is that this case may firmly be anchored in the the paradigm of inference relation of a qconsequence. The latter was constructed to formalize a reasoning which from nonrejected premisses leads to the accepted conclusions. A corresponding structural qconsequence operation felt apart from the Tarski paradigm of consequence and, finally appeared inferentially threevalued, thus violating the Suszko's thesis on logical twovaluedness.
The threevalued version of FA is first applied to logic algebras and matrices, and then to inference calculi defined or characterized by their use. The main result says that an inferential calculus (L,W) satisfies the threevalued version of FA if and if it is exclusively complete with respect to a class of notreducible threeelement matrices.
We believe that the proposal opens further possibilities for exploration of classes of models of logically threevalued inferential calculi having such characteristics.

Authors:
Edward NIEZNANSKI
Title:Elements of Modal Theodicy
Pages:253264
File:bibtex
Abstract ( + )
The aim of the presented study is to present a certain point of view within the framework of discussion about the problem of the appearance of existential evil (metaphysical and physical) before the omniscience and goodness of God. On the philosophical level the conducted analysis is inspired by conceptions of G. W. Leibniz. As a result of the considerations a formalized system is obtained, the system that for the notions of omniscience and omnipotence determines the formal properties accordingly: $KT$ and S4modalities. Within the confines of the constructed theory, among others, one can precise and deny religious fatalism and predestination fallacies. The formalization interpreted in the semantics of possible worlds constitutes an attempt to accomplish a task set by Swinburne for the theists' followers  the task to solve the aporia resulting from the existence of evil and the existence of divine attributes of omnipotence and omniscience.

Authors:
Marek NOWAK
Title:The Logics of Analytic Equivalence
Pages:265272
File:bibtex
Abstract ( + )
A notion of socalled analytic equivalence is considered, in the form of Suszko's connective of propositional identity. Two axiomatic strengthenings of the Sentential Calculus with Identity of Suszko involving that connective are presented. Both realize the following principle due to Wojcicki: two sentences whose logical forms in sentential language are logically equivalent and have the same sentential variables, express the same propositions

Authors:
Jan WOLENSKI
Title:Remarks on Identity Across Possible Worlds
Pages:273287
File:bibtex
Abstract ( + )
Since our world could be otherwise than it was, is and will be, we might consider objects and their properties in other configurations than they actually occur. This means that other stories about our world, different than the actual narration, are fairly possible. For example, Aristotle could remain in Stagira and become a physician like his father. Thus, we have Aristotle in the real world and Aristotle in a possible world. Are both identical or different persons? If we affirmatively answer this question, we automatically admit identity as acting across possible worlds or transworld identity. This paper argues for the negative answer: there is no transworld identity, unless we apply a very abstract modeltheoretic approach.