Alternative axiomatics and complexity of deliberative STIT theories

We propose two alternatives to Xu's axiomatization of the Chellas STIT. The first one also provides an alternative axiomatization of the deliberative STIT. The second one starts from the idea that the historic necessity operator can be defined as an abbreviation of operators of agency, and can thus be eliminated from the logic of the Chellas STIT. The second axiomatization also allows us to establish that the problem of deciding the satisfiability of a STIT formula without temporal operators is NP-complete in the single-agent case, and is NEXPTIME-complete in the multiagent case, both for the deliberative and the Chellas' STIT.Comment: Submitted to the Journal of Philosophical Logic; 13 pages excluding anne

Deontic ‘cocktail’ according to E. Mally’s receipt

In 1926, Ernst Mally, an Austrian logician, has introduced a system of deontic logic in which he has proposed three fundamental distinctions which proved to be important in the context of the further development of the logic of norms. It is argued that in his philosophical considerations Mally has introduced a number of important distinctions concerning the very concept of norm, but by getting them confused in introducing the subsequent formalisms he failed to formally preserve them. In some of his philosophically made distinctions Mally apparently foresaw contemporary trends in logic of norms. To some extent this particular feature of Mally’s system open wide opportunities to reconstruct –– with the corresponding renovations — his illformed Deontik into many nowadays known systems of logic of norms and thus provides a fertile ground for this kind of research

Karma Theory, Determinism, Fatalism and Freedom of Will

The so-called theory of karma is one of the distinguishing aspects of Hinduism and other non-Hindu south-Asian traditions. At the same time that the theory can be seen as closely connected with the freedom of will and action that we humans supposedly have, it has many times been said to be determinist and fatalist. The purpose of this paper is to analyze in some deepness the relations that are between the theory of karma on one side and determinism, fatalism and free-will on the other side. In order to do that, I shall use what has been described as the best formal approach we have to indeterminism: branching time theory. More specifically, I shall introduce a branching time semantic framework in which, among other things, statements such as “state of affairs e is a karmic effect of agent a”, “a wills it to be the case that e” and “e is inevitable” could be properly represented

Non-normal modalities in variants of Linear Logic

This article presents modal versions of resource-conscious logics. We concentrate on extensions of variants of Linear Logic with one minimal non-normal modality. In earlier work, where we investigated agency in multi-agent systems, we have shown that the results scale up to logics with multiple non-minimal modalities. Here, we start with the language of propositional intuitionistic Linear Logic without the additive disjunction, to which we add a modality. We provide an interpretation of this language on a class of Kripke resource models extended with a neighbourhood function: modal Kripke resource models. We propose a Hilbert-style axiomatization and a Gentzen-style sequent calculus. We show that the proof theories are sound and complete with respect to the class of modal Kripke resource models. We show that the sequent calculus admits cut elimination and that proof-search is in PSPACE. We then show how to extend the results when non-commutative connectives are added to the language. Finally, we put the logical framework to use by instantiating it as logics of agency. In particular, we propose a logic to reason about the resource-sensitive use of artefacts and illustrate it with a variety of examples

Seeing to it that an agent forms a belief

To what extent, if any, is belief formation under our direct voluntary control? In the present paper, it is suggested that an understanding of ascriptions of an agent α’s belief formation can be obtained by considering ascriptions of α’s seeing to it that α has certain implicit beliefs. It will turn out that, contrary to what doxastic anti-voluntarists such as B. Williams have claimed, a consistent formal treatment of ascriptions of belief formation, understood as decisions to believe, is possible

Agency and fictional truth: a formal study on fiction-making

Fictional truth, or truth in fiction/pretense, has been the object of extended scrutiny among philosophers and logicians in recent decades. Comparatively little attention, however, has been paid to its inferential relationships with time and with certain deliberate and contingent human activities, namely, the creation of fictional works. The aim of the paper is to contribute to filling the gap. Toward this goal, a formal framework is outlined that is consistent with a variety of conceptions of fictional truth and based upon a specific formal treatment of time and agency, that of so-called stit logics. Moreover, a complete axiomatic theory of fiction-making TFM is defined, where fiction-making is understood as the exercise of agency and choice in time over what is fictionally true. The language L of TFM is an extension of the language of propositional logic, with the addition of temporal and modal operators. A distinctive feature of L with respect to other modal languages is a variety of operators having to do with fictional truth, including a \u2018fictionality\u2019 operator M (to be read as \u201cit is a fictional truth that\u201d). Some applications of TFM are outlined, and some interesting linguistic and inferential phenomena, which are not so easily dealt with in other frameworks, are accounted for

ЧТО НУЖНО СДЕЛАТЬ ДЛЯ ЛОГИКИ ИМПЕРАТИВОВ

This paper presents the logical treatment of imperatives (commands and promises) regarded as actions one rational agent performs in order to compel the other rational agent, by imposing certain obligations on her, to act in a certain way. To talk about the embedded stit-formulas that represent such imperative actions the framework of stit-logic supplied with the ⃝-operator, as it is introduced by J. Horty, is used. We investigate some curious technical details of using the ⃝-operator ranging over the set of agents along with differingent  stit-operators and suggest formulas picturing some properties typical for the usage of commands and promises. We establish several theorems and propositions expressing essential principles of imperative agency and show that these principles differ substantially from their analogs in propositional logic and standard deontic logic (SDL). Finally, we briefly discuss the possibilities of further investigation that embodies such issues as expressing the imperative permission and prevalent embedded imperatives in the given framework.В статье представлен логический подход к императивам (командам и обещаниям), которые трактуются как действия одного рационального агента, направленные на то, чтобы побудить другого рационального агента, посредством связывания его обязательствами определенного рода, к совершению некоторого поступка. Для того, чтобы иметь возможность интерпретировать формулы с вложенными агентными операторами, которые отражают таким образом понимаемые императивы, используется STIT-логика, дополненная деонтическим оператором «О» хортиевского типа. В статье исследуется ряд любопытных технических деталей, связанных с использованием деонтического оператора в рамках логики действия совместно с различными агентными операторами, и предлагаются формулы, отражающие характеристические свойства использования команд и обещаний. Мы формулируем несколько теорем и наблюдений, отражающих существенные свойства употребления императивов, и показываем, что между ними и сходными с ними утверждениями из пропозициональной и стандартной деонтической логики отсутствует параллелизм. В заключении мы кратко обсуждаем перспективы будущих исследований в этой области, касающихся представления императивного разрешения и широко распространенных вложенных императивных действий

ON THE INTENTIONALITY AND IMPERFECT BUT MINIMAL RATIONALITY OF HUMAN SPEAKERS

I will criticize the current logical analysis of attitudes due to J. Hintikka (1971) according to which human agents are either perfectly rational or completely irrational. I will present the principles of a general logic of first level attitudes and actions that accounts for our intentionality and imperfect but minimal rationality. First level attitudes and actions are attitudes and actions of individual agents at a single moment of time. In my approach psychological modes of propositional attitudes have other components than their basic Cartesian category of cognition and volition. I will formulate a recursive definition of the set of all psychological modes. I will also analyze the nature of complex first level attitudes such as conditional attitudes and sums and denegations of attitudes which are irreducible to propositional attitudes. My primary purpose here will be first to explicate inductively conditions of possession and of satisfaction of all first level attitudes and to integrate my logic of attitudes within a general theory of first level actions explicating the primacy of intentional actions, their conditions of success and fundamental laws of action generation. For that purpose I will use a non classical predicative propositional logic and consider subjective as well as objective possibilities. Agents of voluntary actions and illocutionary acts have intentions and other first level attitudes. I will explain why logically equivalent propositions are not the content of the same attitudes and intentional actions and why human agents are neither logically omniscient nor perfectly rational but always remain minimally rational in the exercise of thought and the use of language. For more information see my next book Speech Acts in Dialogue

Temporal STIT logic and its application to normative reasoning

International audienceI present a variant of STIT with time, called T-STIT (Temporal STIT), interpreted in standard Kripke semantics. On the syntactic level, T-STIT is nothing but the extension of atemporal individual STIT by: (i) the future tense and past tense operators, and (ii) the operator of group agency for the grand coalition (the coalition of all agents). A sound and complete axiomatisation for T-STIT is given. Moreover, it is shown that T-STIT supports reasoning about interesting normative concepts such as the concepts of achievement obligation and commitment

Arguing about Free Will: Lewis and the Consequence Argument

I explore some issues in the logics and dialectics of practical modalities connected with the Consequence Argument (CA) considered as the best argument for the incompatibility of free will and determinism. According to Lewis (1981) in one of the possible senses of (in)ability, the argument is not valid; however, understood in the other of its possible senses, the argument is not sound. This verdict is based on the assessment of the modal version of the argument, where the crucial notion is power necessity (“no choice” operator), while Lewis analyses the version where the central notion is the locution “cannot render false.”Lewis accepts closure of the relevant (in)ability operator under entailment but not closure under implication. His strategy has a seemingly strange corollary: a free predetermined agent is able (in a strong, causal sense) to falsity the conjunction of history and law. I compare a Moorean position with respect to radical skepticism and knowledge closure with ability closure and propose to explain Lewis’s strategy in the framework of his Moorean stance