Deontic logic is devoted to the study of logical properties of normative predicates such as permission, obligation and prohibition. Since it is usual to apply these predicates to actions, many deontic logicians have proposed formalisms where actions and action combinators are present. Some standard action combinators are action conjunction, choice between actions and not doing a given action. These combinators resemble boolean operators, and therefore the theory of boolean algebra offers a well-known athematical framework to study the properties of the (...) classic deontic operators when applied to actions. In his seminal work, Segerberg uses constructions coming from boolean algebras to formalize the usual deontic notions. Segerberg’s work provided the initial step to understand logical properties of deontic operators when they are applied to actions. In the last years, other authors have proposed related logics. In this chapter we introduce Segerberg’s work, study related formalisms and investigate further challenges in this area. (shrink)
Within the scope of interest of deontic logic, systems in which names of actions are arguments of deontic operators (deontic action logic) have attracted less interest than purely propositional systems. However, in our opinion, they are even more interesting from both theoretical and practical point of view. The fundament for contemporary research was established by K. Segerberg, who introduced his systems of basic deontic logic of urn model actions in early 1980s. Nowadays such logics are considered mainly within propositional dynamic (...) logic (PDL). Two approaches can be distinguished: in one of them deontic operators are introduced using dynamic operators and the notion of violation, in the other at least some of them are taken as primitive. The second approach may be further divided into the systems based on Boolean algebra of actions and the systems built on the top of standard PDL. In the present paper we are interested in the systems of deontic action logic based on Boolean algebra. We present axiomatizations of six systems and set theoretical models for them. We also show the relations among them and the position of some existing theories on the resulting picture. Such a presentation allows the reader to see the spectrum of possibilities of formalization of the subject. (shrink)
Building on our diverse research traditions in the study of reasoning, language and communication, the Polish School of Argumentation integrates various disciplines and institutions across Poland in which scholars are dedicated to understanding the phenomenon of the force of argument. Our primary goal is to craft a methodological programme and establish organisational infrastructure: this is the first key step in facilitating and fostering our research movement, which joins people with a common research focus, complementary skills and an enthusiasm to work (...) together. This statement—the Manifesto—lays the foundations for the research programme of the Polish School of Argumentation. (shrink)
In the paper we present a formal system motivated by a specific methodology of creating norms. According to the methodology, a norm-giver before establishing a set of norms should create a picture of the agent by creating his repertoire of actions. Then, knowing what the agent can do in particular situations, the norm-giver regulates these actions by assigning deontic qualifications to each of them. The set of norms created for each situation should respect (1) generally valid deontic principles being the (...) theses of our logic and (2) facts from the ontology of action whose relevance for the systems of norms we postulate. (shrink)
The aim of the paper is to point out the modelling choices that lead to different systems of deontic action logic. A kind of a roadmap is presented. On the one hand it can help the reader to find the deontic logic appropriate for an intended application relying on the information considering the way in which a deontic logic represents actions and how it characterises deontic properties in relation to (the representation of) actions. On the other hand it is a (...) guideline how to build a deontic action logic which satisfies the desired properties. (shrink)
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. (shrink)
A calculus of names is a logical theory describing relations between names. By a pure calculus of names we mean a quantifier-free formulation of such a theory, based on classical propositional calculus. An axiomatisation of a pure calculus of names is presented and its completeness is discussed. It is shown that the axiomatisation is complete in three different ways: with respect to a set theoretical model, with respect to Leśniewski's Ontology and in a sense defined with the use of axiomatic (...) rejection. The independence of axioms is proved. A decision procedure based on syntactic transformations and models defined in the domain of only two members is defined. (shrink)
By pure calculus of names we mean a quantifier-free theory, based on the classical propositional calculus, which defines predicates known from Aristotle’s syllogistic and Leśniewski’s Ontology. For a large fragment of the theory decision procedures, defined by a combination of simple syntactic operations and models in two-membered domains, can be used. We compare the system which employs `ε’ as the only specific term with the system enriched with functors of Syllogistic. In the former, we do not need an empty name (...) in the model, so we are able to construct a 3-valued matrix, while for the latter, for which an empty name is necessary, the respective matrices are 4-valued. (shrink)
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. (shrink)
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. (shrink)
The paper offers a logical characterisation of multi-step actions in the context of deontic notions of obligation, permission and prohibition. Deontic notions for sequentially composed actions are founded on deontic notions for one-step actions. The present work includes a formal study of situations where execution of a multi-step action has been unsuccessful and provides normative analysis of such actions.
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. (shrink)
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. (shrink)
We investigate a speci c 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 speci cation using the tools from applied ontology { RDF format for information and the Protege editor. (shrink)
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. (shrink)
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. (shrink)
In the paper we discuss different intuitions about the properties of obligatory actions in the framework of deontic action logic based on boolean algebra. Two notions of obligation are distinguished–abstract and processed obligation. We introduce them formally into the system of deontic logic of actions and investigate their properties and mutual relations.
The paper tackles the problem of the relation between rights and obligations. Two examples of situations in which such a relation occurs are discussed. One concerns the abortion regulations in Polish law, the other one—a clash between freedom of expression and freedom of enterprise occurring in the context of discrimination. The examples are analysed and formalised using labelled transition systems in the \ framework. Rights are introduced to the system as procedures allowing for their fulfilment. Obligations are based on the (...) requirement of cooperation in the realisation of the goals of the agent that has a right. If the right of an agent cannot be fulfilled without an action of another agent, then that action is obligatory for that agent. If there are many potential contributors who are individually allowed to refuse, then the last of them is obliged to help when all the others have already refused. By means of formalisation this account of the relation under consideration is precisely expressed and shown consistent. (shrink)
