Action logic of Pratt [21] can be presented as Full Lambek Calculus FL [14, 17] enriched with Kleene star *; it is equivalent to the equational theory of residuated Kleene algebras (lattices). Some results on axiom systems, complexity and models of this logic were obtained in [4, 3, 18]. Here we prove a stronger form of *-elimination for the logic of *-continuous action lattices and the –completeness of the equational theories of action lattices of (...) subsets of a finite monoid and action lattices of binary relations on a finite universe. We also discuss possible applications in linguistics. (shrink)

This article examines how the action logics associated with the stages of consciousness development of organizational leaders can influence the meaning, which these leaders give to corporate greening and their capacity to consider the specific complexities, values, and demands of environmental issues. The article explores how the seven principal action logics identified by Rooke and Torbert (2005, Harvard Business Review 83 (4), 66–76; Opportunist, Diplomat, Expert, Achiever, Individualist, Strategist and Alchemist) can affect environmental leadership. An examination of the (...) strengths and limitations of these action logics reveals the relevance of the so-called post-conventional stages of consciousness to the recognition and effective management of complex environmental issues. Suggestions are also made for promoting organizational contexts conducive to the development of a post-conventional environmental leadership. (shrink)

In this paper we present an executable approach to model interactions between agents that involve sensitive, privacy-related information. The approach is formal and based on deontic, epistemic and action logic. It is conceptually related to the Belief-Desire-Intention model of Bratman. Our approach uses the concept of sphere as developed by Waltzer to capture the notion that information is provided mostly with restrictions regarding its application. We use software agent technology to create an executable approach. Our agents hold beliefs (...) about the world, have goals and commitment to the goals. They have the capacity to reason about different courses of action, and communicate with one another. The main new ingredient of our approach is the idea to model information itself as an intentional agent whose main goal it is to preserve the integrity of the information and regulate its dissemination. We demonstrate our approach by applying it to an important process in the insurance industry: applying for a life insurance. In this paper we will: (1) describe the challenge organizational complexity poses in moral reasoning about informational relationships; (2) propose an executable approach, using software agents with reasoning capacities grounded in modal logic, in which moral constraints on informational relatio nships can be modeled and investigated; (3) describe the details of our approach, in which information itself is modeled as an intentional agent in its own right; (4) test and validate it by applying it to a concrete ‘hard case’ from the insurance industry; and (5) conclude that our approach upholds and offers potential for both research and practical application. (shrink)

The semantics for a deontic action logic based on Boolean algebra is extended with an interpretation of action expressions in terms of sets of alternative actions, intended as a way to model choice. This results in a non-classical interpretation of action expressions, while sentences not in the scope of deontic operators are kept classical. A deontic structure based on Simons’ supercover semantics is used to interpret permission and obligation. It is argued that these constructions provide ways (...) to handle various problems related to free choice permission. The main result is a sound and complete axiomatization of the semantics. (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)

Infinitary action logic can be naturally expanded by adding exponential and subexponential modalities from linear logic. In this article we shall develop infinitary action logic with a subexponential that allows multiplexing (instead of contraction). Both non-commutative and commutative versions of this logic will be considered, presented as infinitary sequent calculi. We shall prove cut admissibility for these calculi, and estimate the complexity of the corresponding derivability problems: in both cases it will turn out to (...) be between complete first-order arithmetic and the \(\omega ^\omega \) level of the hyperarithmetical hierarchy. Here the complexity upper bound is much lower than that for the system with a subexponential that allows contraction. The complexity lower bound in turn is much higher than that for infinitary action logic. (shrink)

In this paper we present an executable approach to model interactions between agents that involve sensitive, privacy-related information. The approach is formal and based on deontic, epistemic and action logic. It is conceptually related to the Belief-Desire-Intention model of Bratman. Our approach uses the concept of sphere as developed by Waltzer to capture the notion that information is provided mostly with restrictions regarding its application. We use software agent technology to create an executable approach. Our agents hold beliefs (...) about the world, have goals and commitment to the goals. They have the capacity to reason about different courses of action, and communicate with one another. The main new ingredient of our approach is the idea to model information itself as an intentional agent whose main goal it is to preserve the integrity of the information and regulate its dissemination. We demonstrate our approach by applying it to an important process in the insurance industry: applying for a life insurance.In this paper we will: (1) describe the challenge organizational complexity poses in moral reasoning about informational relationships; (2) propose an executable approach, using software agents with reasoning capacities grounded in modal logic, in which moral constraints on informational relatio nships can be modeled and investigated; (3) describe the details of our approach, in which information itself is modeled as an intentional agent in its own right; (4) test and validate it by applying it to a concrete ‘hard case’ from the insurance industry; and (5) conclude that our approach upholds and offers potential for both research and practical application. (shrink)

This book gathers together novel essays on the state-of-the-art research into the logic and practice of abduction. In many ways, abduction has become established and essential to several fields, such as logic, cognitive science, artificial intelligence, philosophy of science, and methodology. In recent years this interest in abduction’s many aspects and functions has accelerated. There are evidently several different interpretations and uses for abduction. Many fundamental questions on abduction remain open. How is abduction manifested in human cognition and (...) intelligence? What kinds or types of abduction can be discerned? What is the role for abduction in inquiry and mathematical discovery? The chapters aim at providing answer to these and other current questions. Their contributors have been at the forefront of discussions on abduction, and offer here their updated approaches to the issues that they consider central to abduction’s contemporary relevance. The book is an essential reading for any scholar or professional keeping up with disciplines impacted by the study of abductive reasoning, and its novel development and applications in various fields. (shrink)

We introduce a multimodal framework of deontic action logic which encodes the interaction between two fundamental procedures in normative reasoning: conceptual classification and deontic classification. The expressive power of the framework is noteworthy, since it combines insights from agency logic and dynamic logic, allowing for a representation of many kinds of normative conflicts. We provide a semantic characterization for three axiomatic systems of increasing strength, showing how our approach can be modularly extended in order to get (...) different levels of analysis of normative reasoning. Finally, we discuss ways in which the framework can be used to capture other formalisms proposed in the literature, as well as to model searching problems in Artificial Intelligence. (shrink)

Currently available systems of action deontic logic are not designed to model procedures to assess the conduct of an agent which take into account the intentions of the agent and the circumstances in which she is acting. Yet, procedures of this kind are essential to determine what counts as culpable not doing. In light of this, we design an action logic, AL, in which it is possible to distinguish actions that are objectively possible for an agent, (...) viz. there are no objective impediments for the agent to do them, and actions that, besides being objectively possible, are compatible with the setting or intentions of the agent. (shrink)

Kleene algebras and action logic were proposed to be solutions to the finite axiomatization problem of the algebra of regular sets (of strings). They are treated here as nonclassical logics—with Hilbert-style axiomatizations and semantics. We also provide intuitive accounts in terms of information states of the semantics which provide further insights into the formalisms. The three types of "Kripke-style'' semantics which we define develop insights from gaggle theory, and from our four-valued and generalized Kripke semantics for the minimal (...) substructural logic. Soundness and completeness are proven each time. (shrink)

We introduce a family of tableau calculi for deontic action logics based on finite boolean algebras, these logics provide deontic operators which are applied to a finite number of actions ; furthermore, in these formalisms, actions can be combined by means of boolean operators, this provides an expressive algebra of actions. We define a tableau calculus for the basic logic and then we extend this calculus to cope with extant variations of this formalism; we prove the soundness and (...) completeness of these proof systems. In addition, we investigate the computational complexity of the satisfiability problem for DAL and its extensions; we show this problem is NP-complete when the number of actions considered is fixed, and it is \-Hard when the number of actions is taken as an extra parameter. The tableau systems introduced here can be implemented in PSPACE, this seems reasonable taking into consideration the computational complexity of the logics. (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)

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)

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 article introduces extended models for the propositional dynamic logic PDL. In extended models, valuation assigns to every state a set of atomic formulas and a PDL program. The program is informally construed as an action preferred by a contextually fixed agent. PDL is then extended by introducing a conditional connective expressing partial correctness claims. The main contribution of the article is the observation that the partial correctness conditional is in fact a substructural implication. It is shown that (...) a variant of the minimal distributive substructural logic DB is a fragment of PDLS, an extension of PDL that contains the partial correctness conditional and fusion. It is also shown that the main results can be extended to a specific class of positive substructural logics. (shrink)

Language in Action demonstrates the viability of mathematical research into the foundations of categorial grammar, a topic at the border between logic and linguistics. Since its initial publication it has become the classic work in the foundations of categorial grammar. A new introduction to this paperback edition updates the open research problems and records relevant results through pointers to the literature. Van Benthem presents the categorial processing of syntax and semantics as a central component in a more general (...) dynamic logic of information flow, in tune with computational developments in artificial intelligence and cognitive science. Using the paradigm of categorial grammar, he describes the substructural logics driving the dynamics of natural language syntax and semantics. This is a general type-theoretic approach that lends itself easily to proof-theoretic and semantic studies in tandem with standard logic. The emphasis is on a broad landscape of substructural categorial logics and their proof-theoretical and semantic peculiarities. This provides a systematic theory for natural language understanding, admitting of significant mathematical results. Moreover, the theory makes possible dynamic interpretations that view natural languages as programming formalisms for various cognitive activities. (shrink)

The purpose of this paper is to show that the logical form of action sentences are dependent upon the concept of 'agent' that one takes. A thing type of agent leads to the extensional form while a thinking type of agent leads to intentional form of action sentences. Consequently, it is important to note the locus of the describer who himself is also an agent. If the describer is someone other than theagent, the ascription of action is (...) based on a tacit counterfactual. The agent could have done otherwise, implying the agent to be a being-of-the-world, who acts on the things of the world to bring about a change which could not have occurred otherwise. (shrink)

Over the past decades, logicians interested in rational agency and intelligent interaction studied major components of these phenomena, such as knowledge, belief, and preference. In recent years, standard ‘static’ logics describing information states of agents have been generalized to dynamic logics describing actions and events that produce information, revise beliefs, or change preferences, as explicit parts of the logical system. Van Ditmarsch, van der Hoek & Kooi 2007, Baltag, van Ditmarsch & Moss 2008, van Benthem, to appear A, are up-to-date (...) accounts of this dynamic trend (the present paper follows Chapter 9 of the latter book). But in reality, concrete rational agency contains all these dynamic processes entangled. A concrete setting for this entanglement are games – and this paper is a survey of their interfaces with logic, both static and dynamic. Games are intriguing also since their analysis brings together two major streams, or tribal communities: ‘hard’ mathematical logics of computation, and ‘soft’ philosophical logics of propositional attitudes. Of course, this hard/soft distinction is spurious, and there is no natural border line between the two sources: it is their congenial mixture that makes current theories of agency so lively. (shrink)

Alternating-time temporal logic (ATL) is a branching time temporal logic in which statements about what coalitions of agents can achieve by strategic cooperation can be expressed. Alternating-time temporal epistemic logic (ATEL) extends ATL by adding knowledge modalities, with the usual possible worlds interpretation. This paper investigates how properties of agents’ actions can be expressed in ATL in general, and how properties of the interaction between action and knowledge can be expressed in ATEL in particular. One commonly (...) discussed property is that an agent should know about all available actions, i.e., that the same actions should be available in indiscernible states. Van der Hoek and Wooldridge suggest a syntactic expression of this semantic property. This paper shows that this correspondence in fact does not hold. Furthermore, it is shown that the semantic property is not expressible in ATEL at all. In order to be able to express common and interesting properties of action in general and of the interaction between action and knowledge in particular, a generalization of the coalition modalities of ATL is proposed. The resulting logics, ATL-A and ATEL-A, have increased expressiveness without loosing ATL’s and ATEL’s tractability of model checking. (shrink)

We present Dynamic Epistemic Temporal Logic, a framework for reasoning about operations on multi-agent Kripke models that contain a designated temporal relation. These operations are natural extensions of the well-known “action models” from Dynamic Epistemic Logic. Our “temporal action models” may be used to define a number of informational actions that can modify the “objective” temporal structure of a model along with the agents’ basic and higher-order knowledge and beliefs about this structure, including their beliefs about (...) the time. In essence, this approach provides one way to extend the domain of action model-style operations from atemporal Kripke models to temporal Kripke models in a manner that allows actions to control the flow of time. We present a number of examples to illustrate the subtleties involved in interpreting the effects of our extended action models on temporal Kripke models. We also study preservation of important epistemic-temporal properties of temporal Kripke models under temporal action model-induced operations, provide complete axiomatizations for two theories of temporal action models, and connect our approach with previous work on time in DEL. (shrink)

Information exchange can be viewed as a process of asking questions and answering them. While dynamic epistemic logic traditionally focuses on statements, recent developments have been concerned with ways of incorporating questions. One approach, based on the framework of inquisitive semantics, is inquisitive dynamic epistemic logic ). In this system, agents are represented with issues as well as information. On the dynamic level, it can model actions that raise new issues. Compared to other approaches, a limitation of \ (...) is that it can only encode public announcements. \ can be refined to encode private questions, by merging its static basis, inquisitive epistemic logic ), with action model logic ). This can be done in two ways, namely by enriching action models with questions as possible actions or with issues concerning which action takes place. This paper describes the corresponding dynamic logics, which are conservative extensions of both \ and \, and a sound and complete axiomatization is given for both. (shrink)

A collection of essays in honour of the distinguished philosopher Elizabeth Anscombe.

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)

A new deontic logic, Action Type Deontic Logic, is presented. To motivate this logic, a number of benchmark cases are shown, representing inferences a deontic logic should validate. Some of the benchmark cases are singled out for further comments and some formal approaches to deontic reasoning are evaluated with respect to the benchmark cases. After that follows an informal introduction to the ideas behind the formal semantics, focussing on the distinction between action types and (...) action tokens. Then the syntax and semantics of Action Type Deontic Logic is presented and it is shown to meet the benchmarks. Finally, possibilities for further research are indicated. In the appendix, decidability of the satisfiability of formulas is proved via a technique known from monadic First Order Logic. (shrink)

In this paper I propose and motivate a logic of the interdefined concepts of making true and control, understood as intensional propositional operators to be indexed to an agent. While bearing a resemblance to earlier logics in the tradition, the motivations, semantics, and object language theory differ on crucial points. Applying this logic to widespread formal theories of agency, I use it as a framework to argue against the ubiquitous assumption that the strongest actions or options available to (...) a given agent must always be pairwise incompatible. The conclusion is that this assumption conflicts with failures of higher order control of agents over their degree or precision of control, failures exhibited by such imperfect agents as ourselves. I discuss models in this setting for understanding such imperfectly self-controlling agents. In an appendix, I prove several relevant results about the logic described, including soundness and completeness both for it and for certain natural extensions. (shrink)

This chapter contains sections titled: An Approach to the Logic of Action Normative Act Positions.

The paper presents a logical treatment of actions based on dynamic logic. This approach makes it possible to reflect clearly the differences between static and dynamic elements of the world, a distinction which seems crucial to us for a representation of actions.Starting from propositional dynamic logic a formal system (DLA) is developed, the programs of which are used to model action types. Some special features of this system are: Basic aspects of time are incorporated in DLA as (...) far as they are needed for our purpose. Names for states and for instants are simulated by formulas. It is possible to express formally that a formula is satisfiable or valid. A special program is introduced to reflect developments which are not caused by an official agent but by external influences. (shrink)

1. Logic, perception, and the practical syllogism -- 2. The "physical" structure of the human act -- 3. Internal articulation and force -- 4. The constituents of human action and ignorance thereof -- 5. Intelligibility and the per se -- 6. Action, [phronåesis], and pleasure -- 7. [Phronåesis] and the [phronimos] -- 8. Some other character types.