Piotr Kulicki

Trivalence is quite natural for deontic action logic, where actions are treated as good, neutral or bad.We present the ideas of trivalent deontic logic after J. Kalinowski and its realisation in a 3-valued logic of M. Fisher and two systems designed by the authors of the paper: a 4-valued logic inspired by N. Belnap’s logic of truth and information and a 3-valued logic based on nondeterministic matrices. Moreover, we combine Kalinowski’s idea of trivalence with deontic action logic based on boolean algebra.

In the article attention is paid to the analogy between considerations concerning the number of objects that are the empirical basis for the theory of being and investigations concerning the size of the models necessary for solving formulas on the ground of calculus of names without quantifiers. In both cases a minimum of two objects appear as an answer to the question that has been posed. In explaining the noticed similarity the meaning aspect, as different from the referential aspect of cognition of reality, is pointed to.

In the paper we provide an overview of issues related to the models used in the research on the logic of norms and actions. We present two models of the variability of the world: temporal (acyclic) and atemporal (cyclic). In the first one the past is always clearly defined, and the future is potentially “branched”. The second type of model allows for a return to the situation that took place. Next we describe different approaches towards agency modeling. We present the most important paradigms, including the logic of actions, where actions are interpreted as transitions between the situations and STIT logic, which states only the responsibility of the agent for particular states of affairs. We discuss questions of determinism and indeterminism of actions, identification of basic actions and operations and the issue of identity. The final part of the paper is devoted to deontic categories. In particular, the applicability of the concepts of strong and weak permission and prohibition in different situational contexts, and their relationship to the two concepts of obligation: abstract and derived.

We investigate a specic model of knowledge and beliefs and their dynamics. The model is inspired by public announcement logic and the approach to puzzles concerning knowledge using that logic. In the model epistemic considerations are based on ontology. The main notion that constitutes a bridge between these two disciplines is the notion of epistemic capacities. Within the model we study scenarios in which agents can receive false announcements and can have incomplete or improper views about other agent's epistemic capacities. Moreover, we try to express the description of problem specication using the tools from applied ontology { RDF format for information and the Protege editor.

Aristotle in Analytica Posteriora presented a notion of proof as a special case of syllogism. In the present paper the remarks of Aristotle on the subject are used as an inspiration for developing formal systems of demonstrative syllogistic, which are supposed to formalize syllogisms that are proofs. We build our systems in the style of J. Łukasiewicz as theories based on classical propositional logic. The difference between our systems and systems of syllogistic known from the literature lays in the interpretation of general positive sentences in which the same name occurs twice (of the form SaS). As a basic assumption of demonstrative syllogistic we accept a negation of such a sentence. We present three systems which differ in the interpretation of specific positive sentences in which the same name occurs twice (of the form SiS). The theories are defined as axiomatic systems. For all of them rejected axiomatizations are also supplied. For two of them a set theoretical model is also defined.