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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 (negation is the only operator defined on actions). 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 (parallel execution and free choice) 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.

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... We shall not enter into discussion about algebraical issues here. The interested Reader should consult section 2.3.1 in [24]. 8 Aquist's system F consists of PC laws, Modus Ponens, Substitution rule, Replacement in PC-theorems, and ten axioms: Three of them are mentioned explicitly: ...

... Axioms of the system consist of (16), (18), (20) and the following ones: (16), (24), (25) and (26) characterize relations between deontic concepts as defined in table 5. (18) and (27) characterize prohibition and (20) and (28) state the properties of obligation. ...

Multivalued setting is quite natural for deontic action logic, where actions are usually treated as obligatory, neutral or forbidden. We apply the ideas of multivalued deontic logic to the phenomenon of a moral dilemma and, broader, to any situation where there are conflicting norms. We formalize three approaches towards normative conflicts. We present matrices for the systems and compare their tautologies. Finally, we present a sound and complete axiomatization of the systems.

... He declared that the systems were confluent but did not provide the proof. The adequacy of K 1 with respect to a model based on boolean algebra, corresponding to Kalinowski's intuitions presented in an informal way in [4], has recently been proved in [9]. In the present paper we prove the adequacy of the two Kalinowski's original approaches. ...

Jerzy Kalinowski's K1 logic is one of the frst systems of deontic logic. Kalinowski presented it in two forms: as an axiomatic system and with the use of deontic tables analogous to Łukasiewicz's thee-valued propositional logic. Adequacy of those two approaches is proven.

In 1953, Jerzy Kalinowski published his paper on the logic of normative sentences. The paper is recognized as one of the first publications on the formal system of deontic logic. The aim of this paper is to present a tableau system for Kalinowski’s deontic logic and to discuss some of the topics related to the paradoxes of deontic logic.

Here we choose an object-oriented approach to model a deontic action logic. The interpretation of an action, related to its execution circumstance, is a set of events charactered by a structure, named event-base, which satisfies some algebra properties. Different from Modal Action Logic (MAL), this structure is not a Boolean one, but reflects the algebra properties of sequent actions and true concurrent actions. At last, our work includes an axiomatic system for deontic complex actions as well as its completeness.

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.

John Searle's forthcoming book ‘Rationality in Action’ presents a sophisticated and innovative account of the rationality of action. In the book Searle argues against what he calls the classical model of rationality. In the debate that follows Barry Smith challenges some implications of Searle's account. In particular, Smith suggests that Searle's distinction between observer-relative and observer–independent facts of the world is ill suited to accommodate moral concepts. Leo Zaibert takes on Searle's notion of the gap. The gap exists between the reasons that we have for acting and our actions. According to Searle, whenever there is no gap, our actions exhibit irrationality. Zaibert points out a certain obscurity in Searle's treatment of the gap, particularly in connection with Searle's notion of ‘recognitional rationality’. Finally, Josef Moural examines the interactions between Searle's theory of institutions and his theory of rationality, with emphasis on the connections between intentionality and Searle's notion of the ‘background’.

This volume describes and analyzes in a systematic way the great contributions of the philosopher Krister Segerberg to the study of real and doxastic actions. Following an introduction which functions as a roadmap to Segerberg's works on actions, the first part of the book covers relations between actions, intentions and routines, dynamic logic as a theory of action, agency, and deontic logics built upon the logics of actions. The second section explores belief revision and update, iterated and irrevocable beliefs change, dynamic doxastic logic and hypertheories.
Segerberg has worked for more than thirty years to analyze the intricacies of real and doxastic actions using formal tools - mostly modal (dynamic) logic and its semantics. He has had such a significant impact on modal logic that "It is hard to roam for long in modal logic without finding Krister Segerberg's traces," as Johan van Benthem notes in his chapter of this book.

“There is no such thing as philosophical logic”, Wittgenstein said in a letter to C. K. Ogden.1 In spite of his veto the term now has an established use. It could be defined as signifying the applications of the tools of formal logic to the analysis of concepts and conceptual structures in which philosophers traditionally have taken interest. Pursuits in this spirit sometimes shed interesting light on old problems. More often perhaps they give rise to new problems and steer the interest of philosophers in new directions.

The aim of this article is to construct a deontic logic in which the free choice postulate [11] would be consistent and all the implausible result mentioned in [5] will be blocked. To achieve this we first developed a new theory of action. Then we build a new deontic logic in which the deontic action operator and the deontic proposition operator are explicitly distinguished.

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.

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 practi-cal 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 distin-guished: 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.

The formal language studied in this paper contains two categories of expressions, terms and formulas. Terms express events, formulas propositions. There are infinitely many atomic terms and complex terms are made up by Boolean operations. Where and are terms the atomic formulas have the form = ( is the same as ), Forb ( is forbidden) and Perm ( is permitted). The formulae are truth functional combinations of these. An algebraic and a model theoretic account of validity are given and an axiomatic system is provided for which they are characteristic.The closure principle, that what is not forbidden is permitted is shown to hold at the level of outcomes but not at the level of events. In the two final sections some other operators are considered and a semantics in terms of action games.

Dynamic deontic logics reduce normative assertions about explicit complex actions to standard dynamic logic assertions about the relation between complex actions and violation conditions. We address two general, but related problems in this field. The first is to find a formalization of the notion of ‘action negation’ that (1) has an intuitive interpretation as an action forming combinator and (2) does not impose restrictions on the use of other relevant action combinators such as sequence and iteration, and (3) has a meaningful interpretation in the normative context. The second problem we address concerns the reduction from deontic assertions to dynamic logic assertions. Our first point is that we want this reduction to obey the free-choice semantics for norms. For ought-to-be deontic logics it is generally accepted that the free-choice semantics is counter-intuitive. But for dynamic deontic logics we actually consider it a viable, if not, the better alternative. Our second concern with the reduction is that we want it to be more liberal than the ones that were proposed before in the literature. For instance, Meyer's reduction does not leave room for action whose normative status is neither permitted nor forbidden. We test the logics we define in this paper against a set of minimal logic requirements.

We introduce a deontic action logic and its axiomatization. This logic has some useful properties (soundness, completeness, compactness and decidability), extending the properties usually associated with such logics. Though the propositional version of the logic is quite expressive, we augment it with temporal operators, and we outline an axiomatic system for this more expressive framework. An important characteristic of this deontic action logic is that we use boolean combinators on actions, and, because of finiteness restrictions, the generated boolean algebra is atomic, which is a crucial point in proving the completeness of the axiomatic system. As our main goal is to use this logic for reasoning about fault-tolerant systems, we provide a complete example of a simple application, with an attempt at formalization of some concepts usually associated with fault-tolerance.

Halldén, in [1], has recently pointed out that it is highly undesirable, in a system of sentential calculus, for there to exist two formulas α and β such that: (i) α and β contain no variable in common; (ii) neither α nor β is provable; (iii) α ∨ β is provable. We shall call a system unreasonable ( in the sense of Halldén ) if there exists a pair of formulas α and β having properties (i), (ii), and (iii). Halldén shows (in [1]) that the Lewis systems S 1 and S 3 are unreasonable in this sense; and that the same is true of any system which is between S 1 and S 3, as well as of every system which is stronger than S 3 but weaker than both S 4 and S 7. In the present note we shall show that this defect does not occur in S 4, nor in S 5, nor in any “quasi-normal” extension of S 5; we give an example, on the other hand, of an unreasonable system which lies between S 4 and S 5.
When we speak, in what follows, of a system of modal logic , we shall mean a system having the same class of well-formed formulas as have the various Lewis calculi. Thus the well-formed formulas of a system of modal logic, when written in unabbreviated form, are just those formulas which can be built up from sentential variables by use of the binary connective ‘·’ (conjunction sign), and the two unary connectives ‘˜’ (negation sign) and ‘◇’ (possibility sign). We shall, however, also make use of some of the defined signs of Lewis.

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