Piotr Kulicki

The paper tackles two problems. The first one is to grasp the real meaning of Jerzy Kalinowski’s theory of normative sentences. His formal system K 1 is a simple logic formulated in a very limited language . While presenting it Kalinowski formulated a few interesting philosophical remarks on norms and actions. He did not, however, possess the tools to formalise them fully. We propose a formulation of Kalinowski’s ideas with the use of a set-theoretical frame similar to the one presented by Krister Segerberg in his A Deontic Logic of Action. At the same time we enrich the language used by Kalinowski with more operators on actions and present an adequate axiomatisation of the resulting system. That allows us to disclose some unrevealed aspects of Kalinowski’s theory. The most important one is a relation between acts which we call moral indiscernibility. Our second problem is a proper understanding of moral indiscernibility. We show how a repertoire of agent’s actions, defined with the use of simple observable elements of actions, can be filtrated by the relation of moral indiscernibility. That allows us to understand the consequences of Kalinowski’s claim that not doing something good is always bad

This paper tackles the problem of inference in normative systems where norms concerning actions and states of affairs appear together. A deontic logic of actions and states is proposed as a solution. It is made up of two independent deontic logics, namely a deontic logic of action and a deontic logic of states, interlinked by bridging definitions. It is shown at a language and a model level how an agent should look for norms to follow in a concrete situation. It is pointed out that such specific norms are obtained by finding the most specific obligation and the most general prohibition. They are to be derived from all norms applicable to the situation by using the principles of the logic presented in this paper.

In the paper we examine the method of axiomatic rejection used to describe the set of nonvalid formulae of Aristotle's syllogistic. First we show that the condition which the system of syllogistic has to fulfil to be ompletely axiomatised, is identical to the condition for any first order theory to be used as a logic program. Than we study the connection between models used or refutation in a first order theory and rejected axioms for that theory. We show that any formula of syllogistic enriched with classical connectives is decidable using models in the domain with three members.

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.