Possible Worlds Framework Research Articles

Review

Review

Impossible worlds and logical omniscience: an impossibility result

In this paper, I investigate whether we can use a world-involving framework to model the epistemic states of non-ideal agents. The standard possible-world framework falters in this respect because of a commitment to logical omniscience. A familiar attempt to overcome this problem centers around the use of impossible worlds where the truths of logic can be false. As we shall see, if we admit impossible worlds where “anything goes” in modal space, it is easy to model extremely non-ideal agents that are incapable of performing even the most elementary logical deductions. A much harder, and considerably less investigated challenge is to ensure that the resulting modal space can also be used to model moderately ideal agents that are not logically omniscient but nevertheless logically competent. Intuitively, while such agents may fail to rule out subtly impossible worlds that verify complex logical falsehoods, they are nevertheless able to rule out blatantly impossible worlds that verify obvious logical falsehoods. To model moderately ideal agents, I argue, the job is to construct a modal space that contains only possible and non-trivially impossible worlds where it is not the case that “anything goes”. But I prove that it is impossible to develop an impossible-world framework that can do this job and that satisfies certain standard conditions. Effectively, I show that attempts to model moderately ideal agents in a world-involving framework collapse to modeling either logical omniscient agents, or extremely non-ideal agents.

Modality (review)

Reviewed by: Modality Valentine Hacquard Modality. By Paul Portner. (Oxford surveys in semantics and pragmatics.) Oxford: Oxford University Press, 2009. Pp. xi, 288. ISBN 9780199292424. $120 (Hb). Paul Portner’s Modality is the first volume of Oxford’s new ‘Surveys in semantics and pragmatics’ series, which is designed to provide ‘both a valuable resource for instruction and reference and a state-of-the-art perspective on contemporary semantic and pragmatic theory from the experts shaping the field’ (xi). And Modality lives up to this billing. It serves as an introduction, giving an overview of the main theories of modality, from modal logic, through Angelika Kratzer’s seminal work (Kratzer 1981, 1991), to more recent approaches. Here P manages to explain both the forest and the trees, illuminating, for each theory, both its intuitive appeal and its formal details. But the book is also a valuable reference for experts. It summarizes major areas of active debates (e.g. truth-conditional status of epistemic modality), presents novel issues and challenges to current theories (e.g. issues of graded modality), and offers new solutions and directions, which will certainly inspire future research. Modality is organized into five chapters. Ch. 1, ‘Introduction’ (1–8), introduces the notion of modality and demonstrates its ubiquity by providing a list of modal expressions. P shows that modality is found across lexical categories, beyond modal auxiliaries and adverbs—on which the book focuses—but also in aspects, tenses, conditionals, and even covertly. Ch. 2 provides an introduction to ‘Modal logic’ (9–46). As P points out, a basic understanding of modal logic is important for linguists working on modality, since this is where the first formal accounts were developed. In this chapter, P presents and motivates the building blocks of the quantification over possible-worlds framework. This introduction is limited, rightly so, given the focus of the book, and because there are many other excellent introductions to modal logic (e.g. Hughes & Cresswell 1996). Ch. 3, ‘Major linguistic theories of modality’ (47–132), presents three main theories of modality: (i) Kratzer’s theory, which is couched in the possible-worlds framework inherited from modal logic and has become the ‘standard’ theory (Section 3.1), (ii) theories of epistemic modality within dynamic semantics (Section 3.2), and (iii) accounts of modality from functional and cognitive linguistics (Section 3.3). The discussion of Kratzer’s theory in Section 3.1 alone makes reading Modality worthwhile. First, the presentation of her theory is extremely clear and should prove very useful to newcomers to modality. It highlights the insights, motivations, and empirical coverage of the theory, while carefully explaining its formal details and spelling out its underlying assumptions. Second, this section contains an important breakthrough for the semantics of graded modality, which will undoubtedly instigate new and exciting research on the topic. As P shows, Kratzer’s system derives graded notions of modality (e.g. better possibility), but it does so in a noncompositional way. P suggests that the key to a compositional solution is to relate grades of modal force to the general theory of gradable expressions, and points to possible ways in which this could be implemented. Ch. 4, ‘Sentential modality’ (133–220), discusses theoretical and empirical issues specific to the semantics of the three main subtypes of modality: (i) epistemic modals, which express possibilities and necessities given what is known; (ii) priority modals, which include deontic, bouletic, and teleological modals—these express possibilities and necessities given certain laws, desires, and goals, respectively; and (iii) dynamic modals, which include ability, volitional, and quantificational modals. Such issues taken together present important challenges to general accounts of modality; for these P suggests a series of solutions that exploit performative aspects of modality. Ch. 5, ‘Modality and other intensional categories’ (221–66), discusses the interaction of modality and tense, looking both at the temporal interpretation of modals and at the intensional component of certain tenses—the association between past tense and counterfactuality as well as between the present and genericity—and the question of whether the future should be thought of as a tense or a modal. It briefly introduces the modality involved in aspectual operators (such as the progressive and the perfect...

A question of commitment

This paper addresses certain restrictions on the use of declaratives as questions in English. Declaratives are taken to express commitment by the speaker, even in a questioning use. The analysis traces the restrictions to two distinct contextual factors: (i) a general principle requiring that a commitment have a recognized source, i.e., a discourse agent who plausibly has independent evidence supporting the content committed to; (ii) specific to a questioning interpretation, the need for the context to support the inference that the speaker’s commitment depends upon the addressee’s anticipated confirmation. Rising intonation contributes a very general element of meaning, indicating that the utterance it marks is contingent upon some discourse condition obtaining; the specific conditions required for a questioning interpretation instantiate one such type of contingency. The proposals are modeled via elaboration of standard contextual structures in a possible-worlds framework.

Determinism and Inevitability

The paper discusses one of the central arguments in Dennett’s Freedom Evolves, an argument designed to show that a deterministic universe would not necessarily be a universe of which it could truly be said that everything that occurs in it is inevitable. It suggests that on its most natural interpretation, the argument is vulnerable to a serious objection. A second interpretation is then developed, but it is argued that without placing more weight on etymological considerations than they can really bear, it can deliver only a significantly qualified version of the conclusion that Dennett is seeking. Moreover, the new argument depends upon an intermediate conclusion which, on the face of it, looks to be self-contradictory. Dennett is able to avoid the appearance of self-contradiction only by utilising a possible-worlds framework for the understanding of “could have done otherwise” judgements which is argued to be unsatisfactory. It is suggested that a different framework might hold the key to understanding how better to defend these same judgements from purported threats from determinism.

RIGID DESIGNATION, DIRECT REFERENCE, AND MODAL METAPHYSICS

Abstract: In this paper I argue that questions about the semantics of rigid designation are commonly and illicitly run together with distinct issues, such as questions about the metaphysics of essence and questions about the theoretical legitimacy of the possible-worlds framework. I discuss in depth two case studies of this phenomenon – the first concerns the relation between rigid designation and reference, the second concerns the application of the notion of rigidity to general terms. I end by drawing out some conclusions about the relations between rigid designation, semantic frameworks, reference, and essence.

Formal Specification and Verification of Multi-Agent Systems

Multi-agent systems are increasingly complex, and the problem of their verification and validation is acquiring increasing importance. In this paper we show how a well known and effective verification technique, model checking, can be generalized to deal with multi-agent systems. This paper explores a particular type of multi-agent system, in which each agent is viewed as having the three mental attitudes of belief (B), desire (D), and intention (I). We use a multi-modal branching-time logic BDICTL, with a semantics that is grounded in traditional decision theory and a possible-worlds framework. A preliminary implementation of the approach shows promising results.

Indicative and Subjunctive Conditionals

Indicative and subjunctive conditionals have different truth conditions. I seek to account for this difference within the general possible-worlds framework developed by Stalnaker and Lewis. I argue that their truth conditions hold for indicative conditionals, and that similar but different conditions hold for subjunctive conditionals. An indicative conditional is true only if its consequent is true in the antecedent-world that is most similar to the actual world overall. A subjunctive conditional is true only if its consequent is true in the antecedent-world that is most similar to the actual world before the antecedent event. A whole set of extant counterexamples to the Stalnaker-Lewis account of subjunctives confirms it for indicatives. This simple development renders similarity theory both more general and more accurate. I also point out that a subjunctive conditional is incorrect in some way if its consequent refers to an earlier time than its antecedent. Indicative and subjunctive independence will be briefly defined and distinguished.'

The case of the exploding perception

My brother, whom we may call Smith, was touring the London Wax Museum. In need of information, he approached a nearby bobby. But no sooner had he started "Excuse me, sir" than he realized, to his own chagrin and his companion's amusement, that he was speaking to a figure of wax. In such a case, we may say, one experiences an 'explosion' of perception: at first Smith sees (is perceptually presen ted with) a bobby, but then that perception 'explodes' and he sees a wax figure. (The imagery stems from Husserl.1) What are we to make of such perceptual 'explosions'? From considerations of the case above, together with some related cases, we shall draw a basic account of the intentionality of perception, an account of the basic intentional or phenomenological structure of seeing an individual. Our account permits an illuminating analysis of these cases of perceptual explosion and so finds motivation and support therein. So goes part I. In part II we pursue a more precise formulation of our characterization of these cases, finding motivation and support for a central part of Hintikka's logic of perception. And in part III we consolidate the results of parts I and II by drawing on Husserl's basic approach to intentionality. An appendix pursues technical aspects in a possible-worlds framework.