Deontic Logic goes back to Ernst Mally’s 1926 work, Grundgesetze des Sollens: Elemente der Logik des Willens [Mally. E.: 1926, Grundgesetze des Sollens: Elemente der Logik des Willens, Leuschner & Lubensky, Graz], where he presented axioms for the notion ‘p ought to be the case’. Some difficulties were found in Mally’s axioms, and the field has much developed. Logic of Knowledge goes back to Hintikka’s work Knowledge and Belief [Hintikka, J.: 1962, Knowledge and Belief: An Introduction to the Logic of (...) the Two Notions, Cornell University Press] in which he proposed formal logics of knowledge and belief. This field has also developed quite a great deal and is now the subject of the TARK conferences. However, there has been relatively little work combining the two notions of knowledge (belief) with the notion of obligation. (See, however, [Lomuscio, A. and Sergot, M.: 2003, Studia Logica 75 63–92; Moore, R. C.: 1990, In J. F. Allen, J. Hendler and A. Tate (eds.), Readings in Planning, Morgan Kaufmann Publishers, San Mateo, CA]) In this paper we point out that an agent’s obligations are often dependent on what the agent knows, and indeed one cannot reasonably be expected to respond to a problem if one is not aware of its existence. For instance, a doctor cannot be expected to treat a patient unless she is aware of the fact that he is sick, and this creates a secondary obligation on the patient or someone else to inform the doctor of his situation. In other words, many obligations are situation dependent, and only apply in the presence of the relevant information. Thus a case for combining Deontic Logic with the Logic of Knowledge is clear. We introduce the notion of knowledge based obligation and offer an S5, history based Kripke semantics to express this notion, as this semantics enables us to represent how information is transmitted among agents and how knowledge changes over time as a result of communications. We consider both the case of an absolute obligation (although dependent on information) as well as the (defeasible) notion of an obligation which may be over-ridden by more relevant information. For instance a physician who is about to inject a patient with drug d may find out that the patient is allergic to d and that she should use d′ instead. Dealing with the second kind of case requires a resort to non-monotonic reasoning and the notion of justified belief which is stronger than plain belief, but weaker than absolute knowledge in that it can be over-ridden. This notion of justified belief also creates a derived notion of default obligation where an agent has, as far as the agent knows, an obligation to do some action a. A dramatic application of this notion is our analysis of the Kitty Genovese case where, in 1964, a young woman was stabbed to death while 38 neighbours watched from their windows but did nothing. The reason was not indifference, but none of the neighbours had even a default obligation to act, even though, as a group, they did have an obligation to take some action to protect Kitty. (shrink)

We present a simple theory of actions against the background of branching time, based on which we propose two versions of an extended stit theory, one equipped with particular actions and the other with sets of such actions. After reporting some basic results of a formal development of such a theory, we briefly explore its connection to a version of branching ETL.

Here is an important new theory of human action, a theory that assumes actions are founded on choices made by agents who face an open future.

John Horty effectively develops deontic logic (the logic of ethical concepts like obligation and permission) against the background of a formal theory of agency. He incorporates certain elements of decision theory to set out a new deontic account of what agents ought to do under various conditions over extended periods of time. Offering a conceptual rather than technical emphasis, Horty's framework allows a number of recent issues from moral theory to be set out clearly and discussed from a uniform point (...) of view. (shrink)

Modal logics, originally conceived in philosophy, have recently found many applications in computer science, artificial intelligence, the foundations of mathematics, linguistics and other disciplines. Celebrated for their good computational behaviour, modal logics are used as effective formalisms for talking about time, space, knowledge, beliefs, actions, obligations, provability, etc. However, the nice computational properties can drastically change if we combine some of these formalisms into a many-dimensional system, say, to reason about knowledge bases developing in time or moving objects. To study (...) the computational behaviour of many-dimensional modal logics is the main aim of this book. On the one hand, it is concerned with providing a solid mathematical foundation for this discipline, while on the other hand, it shows that many seemingly different applied many-dimensional systems (e.g., multi-agent systems, description logics with epistemic, temporal and dynamic operators, spatio-temporal logics, etc.) fit in perfectly with this theoretical framework, and so their computational behaviour can be analyzed using the developed machinery. We start with concrete examples of applied one- and many-dimensional modal logics such as temporal, epistemic, dynamic, description, spatial logics, and various combinations of these. Then we develop a mathematical theory for handling a spectrum of 'abstract' combinations of modal logics - fusions and products of modal logics, fragments of first-order modal and temporal logics - focusing on three major problems: decidability, axiomatizability, and computational complexity. Besides the standard methods of modal logic, the technical toolkit includes the method of quasimodels, mosaics, tilings, reductions to monadic second-order logic, algebraic logic techniques. Finally, we apply the developed machinery and obtained results to three case studies from the field of knowledge representation and reasoning: temporal epistemic logics for reasoning about multi-agent systems, modalized description logics for dynamic ontologies, and spatio-temporal logics. The genre of the book can be defined as a research monograph. It brings the reader to the front line of current research in the field by showing both recent achievements and directions of future investigations (in particular, multiple open problems). On the other hand, well-known results from modal and first-order logic are formulated without proofs and supplied with references to accessible sources. The intended audience of this book is logicians as well as those researchers who use logic in computer science and artificial intelligence. More specific application areas are, e.g., knowledge representation and reasoning, in particular, terminological, temporal and spatial reasoning, or reasoning about agents. And we also believe that researchers from certain other disciplines, say, temporal and spatial databases or geographical information systems, will benefit from this book as well. Key Features: Integrated approach to modern modal and temporal logics and their applications in artificial intelligence and computer science Written by internationally leading researchers in the field of pure and applied logic Combines mathematical theory of modal logic and applications in artificial intelligence and computer science Numerous open problems for further research Well illustrated with pictures and tables. (shrink)

A suggestion is made for representing iterated deontic modalities in stit theory, the “seeing-to-it-that” theory of agency. The formalization is such that normative sentences are represented as agentive sentences and therefore have history dependent truth conditions. In contrast to investigations in alethic modal logic, in the construction of systems of deontic logic little attention has been paid to the iteration... of the deontic modalities.

The purpose of this paper is to explore a new deontic operator for representing what an agent ought to do; the operator is cast against the background of a modal treatment of action developed by Nuel Belnap and Michael Perloff, which itself relies on Arthur Prior's indeterministic tense logic. The analysis developed here of what an agent ought to do is based on a dominance ordering adapted from the decision theoretic study of choice under uncertainty to the present account of (...) action. It is shown that this analysis gives rise to a normal deontic operator, and that the result is superior to an analysis that identifies what an agent ought to do with what it ought to be that the agent does. (shrink)

We present in this paper an axiomatization of Belnap and Perloff's stit theory (a logic of "seeing to it that") with a single agent. The idea of the proof is to apply the notion of companion sets--the same notion as used in another paper by the author that showed the decidability of stit theory with a single agent and Refref equivalence.

Topic of the paper is Q-logic - a logic of agency in its temporal and modal context. Q-logic may be considered as a basal logic of agency since the most important stitoperators discussed in the literature can be defined or axiomatized easily within its semantical and syntactical framework. Its basic agent dependent operator, the Q-operator (also known as Δ- or cstit-operator), which has been discussed independently by E v. Kutschera and B. E Chellas, is investigated here in respect of its (...) relation to other temporal and modal operators. The main result of the paper, then, is a completeness result for a calculus of Q-logic with respect to a semantics defined on the tree-approach to agency as introduced and developed by, among others, E v. Kutschera and N. D. Belnap. (shrink)

The conditional,if an agent did something, then the agent could have done otherwise, is analyzed usingstit theory, which is a logic of seeing to it that based on agents making choices in the context of branching time. The truth of the conditional is found to be a subtle matter that depends on how it is interpreted (e.g., on what otherwise refers to, and on the difference between could and might) and also on whether or not there are busy choosers that (...) can make infinitely many choices in a finite span of time. (shrink)

A prominent issue in mainstream epistemology is the controversy about doxastic obligations and doxastic voluntarism. In the present paper it is argued that this discussion can benefit from forging links with formal epistemology, namely the combined modal logic of belief, agency, and obligation. A stit-theory-based semantics for deontic doxastic logic is suggested, and it is claimed that this is helpful and illuminating in dealing with the mentioned intricate and important problems from mainstream epistemology. Moreover, it is argued that this linking (...) is of mutual benefit. The discussion of doxastic voluntarism directs the attention of doxastic logicians to the notion of belief formation and thus to dynamic aspects of beliefs that have hitherto been neglected. The development of a formal language and semantics for ascriptions of belief formation may contribute to clarifying the contents and the implications of voluntaristic claims. A simple observation concerning other-agent nestings of stit-operators, for instance, may help illuminating the notions of making belief and responsibility for beliefs of others. In this way, stit-theory may serve as a bridge between mainstream and formal epistemology. (shrink)

Topic of the paper is Q-logic – a logic of agency in its temporal and modal context. Q-logic may be considered as a basal logic of agency since the most important stit-operators discussed in the literature can be defined or axiomatized easily within its semantical and syntactical framework. Its basic agent dependent operator, the Q-operator (also known as Δ- or cstit-operator), which has been discussed independently by F. v. Kutschera and B. F. Chellas, is investigated here in respect of its (...) relation to other temporal and modal operators. The main result of the paper, then, is a completeness result for a calculus of Q-logic with respect to a semantics defined on the tree-approach to agency as introduced and developed by, among others, F. v. Kutschera and N. D. Belnap. (shrink)

We investigate a series of logics that allow to reason about agents' actions, abilities, and their knowledge about actions and abilities. These logics include Pauly's Coalition Logic CL, Alternating-time Temporal Logic ATL, the logic of ‘seeing-to-it-that' (STIT), and epistemic extensions thereof. While complete axiomatizations of CL and ATL exist, only the fragment of the STIT language without temporal operators and without groups has been axiomatized by Xu (called Ldm). We start by recalling a simplification of the Ldm that has been (...) proposed in previous work, together with an alternative semantics in terms of standard Kripke models. We extend that semantics to groups via a principle of superadditivity, and give a sound and complete axiomatization that we call Ldm G. We then add a temporal ‘next' operator to Ldm G, and again give a sound and complete axiomatization. We show that Ldm G subsumes coalition logic CL. Finally, we extend these logics with standard S5 knowledge operators. This enables us to express that agents see to something under uncertainty about the present state or uncertainty about which action is being taken. We focus on the epistemic extension of X-Ldm G, noted E-X-Ldm G. In accordance with established terminology in the planning community, we call this extension of X-Ldm G the conformant X-Ldm G. The conformant X-Ldm G enables us to express that agents are able to perform a uniform strategy. We conclude that in that respect, our epistemic extension of X-Ldm G is better suited than epistemic extensions of ATL. (shrink)

We provide a Kripke semantics for a STIT logic with the "next" operator. As the atemporal group STIT is undecidable and unaxiomatizable, we are interested in strict fragments of atemporal group STIT. First we prove that the satisfiability problem of a formula of the fragment made up of individual coalitions plus the grand coalition is also NEXPTIME-complete. We then generalize this result to a fragment where coalitions are in a given lattice. We also prove that if we restrict the language (...) to nested coalitions the satisfiability problem is NP-complete if the number of agents is fixed and PSPACE-complete if the number of agents is variable. Finally we embed individual STIT with the "next" operator into a fragment of atemporal group STIT. (shrink)

But Findlay's remark, like so much that has been written on the subject of time in the present century, was provoked in the first place by McTaggart's ...

We propose two alternatives to Xu’s axiomatization of Chellas’s STIT. The first one simplifies its presentation, and 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 Chellas’s 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 Chellas’s STIT. (shrink)

A structure is described that can serve as a foundation for a semantics for a modal agentive construction such as sees to it that Q ([ stit: Q]). The primitives are Tree,,Instant, Agent, choice. Eleven simple postulates governing this structure are set forth and motivated. Tree and encode a picture of branching time consisting of moments gathered into maximal chains called histories. Instant imposes a time-like ordering. Agent consists of agents, and choice assigns to each agent and each moment in (...) Tree a set of possible choices, where each possible choice is a set of histories. All of these ingredients are referred to in the semantics suggested for [ stit: Q]. The most complex part of the discussion is the motivation for the definition of what it means for a typically non-terminating chain of moments jointly to witness the truth of [ stit: Q] at a moment.The paper begins with an informal account of the Refref conjecture, which says that the only way to refrain from refraining from seeing to something is to see to it. The paper ends with a consideration of an argument of Prior's that in a certain sense contemplation and action are inconsistent. (shrink)

The basic bimodal systemK/K can be interpreted as an analysis of the logic of ability developed in [1]. Where in [1] we would express the claimI can bring it about that P using the formula, with its non-normal operator, we will now use the formula. Here is a normal alethic possibilitation operator.is a normal necessitation operator, but it is independent of, and not subject to an alethic interpretation. Rather, is interpreted to meanI bring it about that P. The result is (...) a simplification and clarification of a combined logic of ability and action like that in [2], but employing only normal operators.A number of extensions of the basic systemK/K are constructed, first by strengthening the two normal sublogics independently and then by linking the two sublogics via axiom schemata involving both operators. The result is a series of increasingly strong systems which more and more adequately fulfill our expectations for a satisfactory logic of action and ability. (shrink)

We develop a multi-agent deontic action logic to study the logical behaviour of two types of deontic conditionals: (1) conditional obligations, having the form "If group H were to perform action aH, then, in group F's interest, group G ought to perform action aG" and (2) conditional permissions, having the form "If group H were to perform action aH, then, in group F's interest, group G may perform action aG". First, we define a formal language for multi-agent deontic action logic (...) and a class of consequentialist models to interpret the formulas of the language. Second, we define a transformation that converts any strategic game into a consequentialist model. Third, we show that an outcome a* is a Nash equilibrium of a strategic game if and only if a conjunction of certain conditional permissions is true in the consequentialist model that results from the transformation of that strategic game. (shrink)

A history of the logic of action is outlined, beginning with St Anselm. Five modern authors are discussed in some detail: von Wright, Fitch, Kanger, Chellas and Pratt.

Two groups of agents, G1 and G2, face a *moral conflict* if G1 has a moral obligation and G2 has a moral obligation, such that these obligations cannot both be fulfilled. We study moral conflicts using a multi-agent deontic logic devised to represent reasoning about sentences like "In the interest of group F of agents, group G of agents ought to see to it that phi". We provide a formal language and a consequentialist semantics. An illustration of our semantics with (...) an analysis of the Prisoner’s Dilemma follows. Next, necessary and sufficient conditions are given for (1) the possibility that a single group of agents faces a moral conflict, for (2) the possibility that two groups of agents face a moral conflict within a single moral code, and for (3) the possibility that two groups of agents face a moral conflict. (shrink)

The purpose of this paper is to prove the decidability ofstit theory (a logic of seeing to it that) with a single agent andRefref Equivalence. This result is obtained through an axiomatization of the theory and a proof that it has thefinite model property. A notion ofcompanions to stit formulas is introduced and extensively used in the proof.

Based on a notion of "companions to stit formulas" applied in other papers dealing with astit logics, we introduce "choice formulas" and "nested choice formulas" to prove the completeness theorems for dstit logics in a language with the dstit operator as the only non-truth-functional operator. The main logic discussed in this paper is the basic logic of dstit with multiple agents, other logics discussed include the basic logic of dstit with a single agent and some logics of dstit with multiple (...) agents each of which corresponds to a semantic condition concerning the number of possible choices for agents. (shrink)

This is a review of John Horty's book, _Agency and Deontic Logic_, OUP 2000.

Recent theories of agency (sees to it that) of Nuel Belnap and Michael Perloff are examined, particularly in the context of an early proposal of the author.