We study classical modal logics with pooling modalities, i.e. unary modal operators that allow one to express properties of sets obtained by the pointwise intersection of neighbourhoods. We discuss salient properties of these modalities, situate the logics in the broader area of modal logics, establish key properties concerning their expressive power, discuss dynamic extensions of these logics and provide reduction axioms for the latter.

Information about the powers and abilities of acting entities is used to coordinate their actions in societies, either physical or digital. Yet, the commonsensical meaning of an acting entity being deemed able to do something is still missing from the existing specification languages for the web or for multi-agent systems. We advance a general purpose abstract logical account of evidence-based ability. A basic model can be thought of as the ongoing trace of a multi-agent system. Every state records systemic confirmations (...) and disconfirmations of whether an acting entity is able to bring about something. Qualitative inductive reasoning is then used in order to infer what acting entities are deemed able to bring about in the multi-agent system. A temporalised modal language is used to talk about deemed ability, actual agency, and confirmation and disconfirmation of deemed ability. What constitutes a confirmation and a disconfirmation is left to the modeller as in general it depends on the application at hand. So to illustrate the methodology we propose two extended examples, one in practical philosophy, the other in system engineering. We first use a logic of agency and ability to obtain a version of Mele’s general practical abilities. Then, we look at the management of abilities in a supervised system. (shrink)

O propósito desse artigo é fornecer um tratamento formal para um tipo de ação até o momento negligenciada nas lógicas modais filosóficas da ação: ação em plano. Ao fazer isso nós seguimos a abordagem padrão nas lógicas modais da ação exemplificados pelos trabalhos de Belnap, Chellas and Pörn. Como nós acreditamos que existe uma relação forte entre plano, tempo e indeterminismo, nós usamos a teoria do tempo ramificado para investigar as características básicas da ação em plano. Além de introduzir uma (...) semântica do tempo ramificado, nós também apresentamos um cálculo correto e completo com relação a essa semântica. DOI:10.5007/1808-1711.2010v14n3p421. (shrink)

Hamblin's Action-State Semantics provides a sound philosophical foundation for understanding the character of the imperative. Taking this as our inspiration, in this paper we present a logic of action, which we call ST, that captures the clear ontological distinction between being responsible for the achievement of a state of affairs and being responsible for the performance of an action. We argue that a relativised modal logic of type RT founded upon a ternary relation over possible worlds integrated with a basic (...) tense logic captures intuitions of the Hamblinian model of imperatives. The logic implements a direct mapping of each of Hamblin's key concepts: strategies, partial strategies and wholehearted satisfaction. (shrink)

Hamblin’s Action-State Semantics provides a sound philosophical foundation for understanding the character of the imperative. Taking this as our inspiration, in this paper we present a logic of action, which we call ST, that captures the clear ontological distinction between being responsible for the achievement of a state of affairs and being responsible for the performance of an action. We argue that a relativised modal logic of type RT founded upon a ternary relation over possible worlds integrated with a basic (...) tense logic captures intuitions of the Hamblinian model of imperatives. The logic implements a direct mapping of each of Hamblin’s key concepts: strategies, partial strategies and wholehearted satisfaction. (shrink)

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 axiomatisation 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 l.. (shrink)

There is little work of a systematic nature in ethical theory or deontic logic on aretaic notions such as praiseworthiness and blameworthiness, despite their centrality to common-sense morality. Without more work, there is little hope of filling the even larger gap of attempting to develop frameworks integrating such aretaic concepts with deontic concepts of common-sense morality, such as what is obligatory, permissible, impermissible, or supererogatory. It is also clear in the case of aretaic concepts that agency is central to such (...) appraisal, so some agential notions must be integrated with aretaic concepts as well. The current paper takes the first step in a larger project aimed at the closure of these gaps. Here I sketch a simple framework for the aretaic appraisal of an agent's performance, layered on top of a simple framework for agency and predetermination. In Part I, I develop the framework for agency, ability, and inevitability, combining elements of work by Brown, Elgesem, Carmo, Santos, and Jones. In Part II, drawing on work by Chisholm and Sosa on intrinsic preferability, I sketch and explore a framework for defining aretaic superiority, praiseworthiness, blameworthiness, neutrality, and indifference, etc., retaining proper links to agency. (shrink)

We introduce and study a PDL-style logic for reasoning about protocols, or plans, under imperfect information. Our paper touches on a number of issues surrounding the relationship between an agent’s abilities, available choices, and information in an interactive situation. The main question we address is under what circumstances can the agent commit to a protocol or plan, and what can she achieve by doing so?

The fact that many modal operators are part of an adjunction is probably folklore since the discovery of adjunctions. On the other hand, the natural idea of a minimal propositional calculus extended with a pair of adjoint operators seems to have been formulated only very recently. This recent research, mainly motivated by applications in computer science, concentrates on technical issues related to the calculi and not on the significance of adjunctions in modal logic. It then seems a worthy enterprise (both (...) for these contemporary topical pursuits and also for historical interest) to trace the concept of adjunction back to the origins of the algebraic semantics of modal logic and to make explicit its ubiquity in this branch of mathematics. (shrink)

In this paper we propose a method for modeling social influence within the STIT approach to action. Our proposal consists in extending the STIT language with special operators that allow us to represent the consequences of an agent’s choices over the rational choices of another agent.

This paper is a preliminary investigation into the application of the formal-logical theory of normative positions to the characterisation of normative-informational positions, pertaining to rules that are meant to regulate the supply of information. First, we present the proposed framework. Next, we identify the kinds of nuances and distinctions that can be articulated in such a logical framework. Finally, we show how such nuances can arise in specific regulations. Reference is made to Data Protection Law and Contract Law, among others. (...) The proposed approach is articulated around two essential steps. The first involves identifying the set of possible interpretations that can be given to a particular norm. This is done by using formal methods. The second involves picking out one of these interpretations as the most likely one. This second step can be resolved only by using further information (e.g., the context or other parts of the regulation). (shrink)

This paper provides a computational framework, based on defeasible logic, to capture some aspects of institutional agency. Our background is Kanger-Lindahl-Pörn account of organised interaction, which describes this interaction within a multi-modal logical setting. This work focuses in particular on the notions of counts-as link and on those of attempt and of personal and direct action to realise states of affairs. We show how standard defeasible logic (DL) can be extended to represent these concepts: the resulting system preserves some basic (...) properties commonly attributed to them. In addition, the framework enjoys nice computational properties, as it turns out that the extension of any theory can be computed in time linear to the size of the theory itself. (shrink)

In this paper we provide a formal analysis of the idea of normative co-ordination. We argue that this idea is based on the assumption that agents can achieve flexible co-ordination by conferring normative positions to other agents. These positions include duties, permissions, and powers. In particular, we explain the idea of declarative power, which consists in the capacity of the power-holder of creating normative positions, involving other agents, simply by proclaiming such positions. In addition, we account also for the concepts (...) of representation, namely the representatives capacity of acting in the name of his principal, and of mandate, which is the mandatees duty to act as the mandator has requested. Finally, we show how the framework can be applied to represent the contract-net protocol. Some brief remarks on future research and applications conclude this contribution. (shrink)

This paper explores the analysis of ability, where ability is to be understood in the epistemic sense—in contrast to what might be called a causal sense. There are plenty of cases where an agent is able to perform an action that guarantees a given result even though she does not know which of her actions guarantees that result. Such an agent possesses the causal ability but lacks the epistemic ability. The standard analysis of such epistemic abilities relies on the notion (...) of action types—as opposed to action tokens—and then posits that an agent has the epistemic ability to do something if and only if there is an action type available to her that she knows guarantees it. We show that these action types are not needed: we present a formalism without action types that can simulate analyzes of epistemic ability that rely on action types. Our formalism is a standard epistemic extension of the theory of “seeing to it that”, which arose from a modal tradition in the logic of action. (shrink)

A number of significant contributions in the last four decades show that non-normal modal logics can be fruitfully employed in several applied fields. Well-known domains are epistemic logic, deontic logic, and systems capturing different aspects of action and agency such as the modal logic of agency, concurrent propositional dynamic logic, game logic, and coalition logic. Semantics for such logics are traditionally based on neighbourhood models. However, other model-theoretic semantics can be used for this purpose. Here, we systematically study multi-relational structures, (...) whose investigation is still relatively underdeveloped. After a brief introduction to two different versions of multi-relational semantics – which we call strong and weak multi-relational semantics – we proceed to study several modal schemata. Special attention is paid to the schemata CON and D. Finally we offer completeness proofs for several systems using both strong and weak semantic tools: The proofs thus cover both classical system.. (shrink)

This paper offers a semantic study in multi-relational semantics of quantified N-Monotonic modal logics with varying domains with and without the identity symbol. We identify conditions on frames to characterise Barcan and Ghilardi schemata and present some related completeness results. The characterisation of Barcan schemata in multi-relational frames with varying domains shows the independence of BF and CBF from well-known propositional modal schemata, an independence that does not hold with constant domains. This fact was firstly suggested for classical modal systems (...) by Stolpe, 557–575, 2003), but unfortunately that work used only models and not frames. (shrink)

We introduce the logic LRC, designed to describe and reason about agents’ abilities and capabilities in using resources. The proposed framework bridges two—up to now—mutually independent strands of literature: the one on logics of abilities and capabilities, developed within the theory of agency, and the one on logics of resources, motivated by program semantics. The logic LRC is suitable to describe and reason about key aspects of social behaviour in organizations. We prove a number of properties enjoyed by LRC and (...) its associated analytic calculus. These results lay at the intersection of the algebraic theory of unified correspondence and the theory of multitype calculi in structural proof theory. Case studies are discussed which showcase several ways in which this framework can be extended and enriched while retaining its basic properties, so as to model an array of issues, both practically and theoretically relevant, spanning from planning problems to the logical foundations of the theory of organizations. (shrink)

This paper investigates the influence that social ties can have on behavior. After defining the concept of social ties that we consider, we introduce an original model of social ties. The impact of such ties on social preferences is studied in a coordination game with outside option. We provide a detailed game theoretical analysis of this game while considering various types of players, i.e., self-interest maximizing, inequity averse, and fair agents. In addition to these approaches that require strategic reasoning in (...) order to reach some equilibrium, we also present an alternative hypothesis that relies on the concept of team reasoning. After having discussed the differences between the latter and our model of social ties, we show how an experiment can be designed so as to discriminate among the models presented in the paper. (shrink)

Belief revision from the point of view of doxastic logic. Logic Journal of the IGPL, 3(4), 535–553. Segerberg, K. (1995). Conditional action. In G. Crocco, L. Fariñas, & A. Herzig (Eds.), Conditionals: From philosophy to computer science, Studies ...

I examine issues in the philosophy of religion at the intersection of what possibilities there are and what a God, as classically conceived in the theistic philosophical tradition, would be able to do. The discussion is centered around arguing for an incompatibility between theism and two principles about possibility and ability, and exploring what theists should say about these incompatibilities. -/- I argue that theism entails that certain kinds and amounts of evil are impossible. This puts theism in conflict with (...) popular principles of modal recombination. However, theists have plausible explanations for the violations of recombination that they posit, and can suitably amend these principles without giving up their usefulness in accounting for what possibilities there are. -/- I also argue that despite the impossibility of these evils, God is able to bring these evils about. This puts theism in conflict with the principle that no one is able to do the impossible. However, theists can give a plausible account of why God is unique in being able to do the impossible, and have distinctive resources to address the arguments in favor of the idea that no one is able to do the impossible. And by denying this principle, theists are able to resolve several otherwise difficult puzzles, including reconciling conflicts between the divine attributes. (shrink)

The 2007 edition of the Amsterdam Colloquium is the Sixteenth in a series which started in 1976. Originally, the Amsterdam Colloquium was an initiative of the Department of Philosophy of the University of Amsterdam. Since 1984 the Colloquium is organized by the Institute for Logic, Language and Computation (ILLC) of the University of Amsterdam.

Overview of fundamental work in deontic logic.

We introduce a number of logics to reason about collective propositional attitudes that are defined by means of the majority rule. It is well known that majoritarian aggregation is subject to irrationality, as the results in social choice theory and judgment aggregation show. The proposed logics for modelling collective attitudes are based on a substructural propositional logic that allows for circumventing inconsistent outcomes. Individual and collective propositional attitudes, such as beliefs, desires, obligations, are then modelled by means of minimal modalities (...) to ensure a number of basic principles. In this way, a viable consistent modelling of collective attitudes is obtained. (shrink)

We carry out the Karttunen-Stalnaker pragmatic account of presupposition projection within a state-of-the art version of dynamic epistemic logic. It turns out that the basic projection facts can all be derived from a Gricean maxim ‘be informative’. This sheds light on a recent controversy on the appropriateness of dynamic semantics as a tool for analysing presupposition.