Comparing Semantics of Logics for Multi-Agent Systems

We draw parallels between several closely related logics that combine — in different proportions — elements of game theory, computation tree logics, and epistemic logics to reason about agents and their abilities. These are: the coalition game logics CL and ECL introduced by Pauly 2000, the alternating-time temporal logic ATL developed by Alur, Henzinger and Kupferman between 1997 and 2002, and the alternating-time temporal epistemic logic ATEL by van der Hoek and Wooldridge (2002). In particular, we establish some subsumption and equivalence results for their semantics, as well as interpretation of the alternating-time temporal epistemic logic into ATL. The focus in this paper is on models: alternating transition systems, multi-player game models (alias concurrent game structures) and coalition effectivity models turn out to be intimately related, while alternating epistemic transition systems share much of their philosophical and formal apparatus. Our approach is constructive: we present ways to transform between different types of models and languages.     

Logics for Epistemic Programs

We construct logical languages which allow one to represent a variety of possible types of changes affecting the information states of agents in a multi-agent setting. We formalize these changes by defining a notion of epistemic program. The languages are two-sorted sets that contain not only sentences but also actions or programs. This is as in dynamic logic, and indeed our languages are not significantly more complicated than dynamic logics. But the semantics is more complicated. In general, the semantics of an epistemic program is what we call aprogram model. This is a Kripke model of ‘actions’,representing the agents' uncertainty about the current action in a similar way that Kripke models of ‘states’ are commonly used in epistemic logic to represent the agents' uncertainty about the current state of the system. Program models induce changes affecting agents' information, which we represent as changes of the state model, called epistemic updates. Formally, an update consists of two operations: the first is called the update map, and it takes every state model to another state model, called the updated model; the second gives, for each input state model, a transition relation between the states of that model and the states of the updated model. Each variety of epistemic actions, such as public announcements or completely private announcements to groups, gives what we call an action signature, and then each family of action signatures gives a logical language. The construction of these languages is the main topic of this paper. We also mention the systems that capture the valid sentences of our logics. But we defer to a separate paper the completeness proof. The basic operation used in the semantics is called the update product. A version of this was introduced in Baltag et al. (1998), and the presentation here improves on the earlier one. The update product is used to obtain from any program model the corresponding epistemic update, thus allowing us to compute changes of information or belief. This point is of interest independently of our logical languages. We illustrate the update product and our logical languages with many examples throughout the paper.     

Temporal and atemporal truth in intuitionistic mathematics

In section 1 we argue that the adoption of a tenseless notion of truth entails a realistic view of propositions and provability. This view, in turn, opens the way to the intelligibility of theclassical meaning of the logical constants, and consequently is incompatible with the antirealism of orthodox intuitionism. In section 2 we show how what we call the potential intuitionistic meaning of the logical constants can be defined, on the one hand, by means of the notion of atemporal provability and, on the other, by means of the operator K of epistemic logic. Intuitionistic logic, as reconstructed within this perspective, turns out to be a part of epistemic logic, so that it loses its traditional foundational role, antithetic to that of classical logic. In section 3 we uphold the view that certain consequences of the adoption of atemporal notion of truth, despite their apparent oddity, are quite acceptable from an antirealist point of view.     

Logical pluralism without the normativity

Logical pluralism is the view that there is more than one logic. Logical normativism is the view that logic is normative. These positions have often been assumed to go hand-in-hand, but we show that one can be a logical pluralist without being a logical normativist. We begin by arguing directly against logical normativism. Then we reformulate one popular version of pluralism—due to Beall and Restall—to avoid a normativist commitment. We give three non-normativist pluralist views, the most promising of which depends not on logic’s normativity but on epistemic goals.

     

Epistemology and artificial intelligence

In this essay we advance the view that analytical epistemology and artificial intelligence are complementary disciplines. Both fields study epistemic relations, but whereas artificial intelligence approaches this subject from the perspective of understanding formal and computational properties of frameworks purporting to model some epistemic relation or other, traditional epistemology approaches the subject from the perspective of understanding the properties of epistemic relations in terms of their conceptual properties. We argue that these two practices should not be conducted in isolation. We illustrate this point by discussing how to represent a class of inference forms found in standard inferential statistics. This class of inference forms is interesting because its members share two properties that are common to epistemic relations, namely defeasibility and paraconsistency. Our modeling of standard inferential statistical arguments exploits results from both logical artificial intelligence and analytical epistemology. We remark how our approach to this modeling problem may be generalized to an interdisciplinary approach to the study of epistemic relations.     

Distributed Knowability and Fitch’s Paradox

Recently predominant forms of anti-realism claim that all truths are knowable. We argue that in a logical explanation of the notion of knowability more attention should be paid to its epistemic part. Especially very useful in such explanation are notions of group knowledge. In this paper we examine mainly the notion of distributed knowability and show its effectiveness in the case of Fitch’s paradox. Proposed approach raised some philosophical questions to which we try to find responses. We also show how we can combine our point of view on Fitch’s paradox with the others. Next we give an answer to the question: is distributed knowability factive? At the end, we present some details concerning a construction of anti-realist modal epistemic logic.     

Abstract argumentation and explanation applied to scientific debates

Abstract argumentation has been shown to be a powerful tool within many fields such as artificial intelligence, logic and legal reasoning. In this paper we enhance Dung’s well-known abstract argumentation framework with explanatory capabilities. We show that an explanatory argumentation framework (EAF) obtained in this way is a useful tool for the modeling of scientific debates. On the one hand, EAFs allow for the representation of explanatory and justificatory arguments constituting rivaling scientific views. On the other hand, different procedures for selecting arguments, corresponding to different methodological and epistemic requirements of theory evaluation, can be formulated in view of our framework.     

A Non-factualist defense of the Reflection principle

Are there plausible synchronic constraints on how a subject thinks of herself extended over time? At first glance, Bas van Fraassen’s principle of Reflection seems to prescribe the sort of epistemic authority one’s future self should be taken by one to have over one’s current epistemic states. (The gist of this principle is that I should now believe what I’m convinced I will believe tomorrow.) There has been a general consensus that, as a principle concerning epistemic authority, Reflection does not apply to epistemically non-ideal agents. I agree with this, but argue here that it misses the point of Reflection. Rather than an epistemic principle concerning reasons for belief, Reflection concerns the semantics of belief avowal. I present a non-factual interpretation of Reflection, argue that the principle provides a constraint on the ways in which one can reflectively endorse one’s future epistemic self, and say something about the logic governing such an interpretation.     

Special issue on radical views on cognition: introduction

In this paper we present the results of a simulation study of credence developments in groups of communicating Bayesian agents, as they update their beliefs about a given proposition p. Based on the empirical literature, one would assume that these groups of rational agents would converge on a view over time, or at least that they would not polarize. This paper presents and discusses surprising evidence that this is not true. Our simulation study shows that these groups of Bayesian agents show group polarization behavior under a broad range of circumstances. This is, we think, an unexpected result, that raises deeper questions about whether the kind of polarization in question is irrational. If one accepts Bayesian agency as the hallmark of epistemic rationality, then one should infer that the polarization we find is also rational. On the other hand, if we are inclined to think that there is something epistemically irrational about group polarization, then something must be off in the model employed in our simulation study. We discuss several possible interfering factors, including how epistemic trust is defined in the model. Ultimately, we propose that the notion of Bayesian agency is missing something in general, namely the ability to respond to higher-order evidence.

     

Reasoning About Games

A mixture of propositional dynamic logic and epistemic logic that we call PDL + E is used to give a formalization of Artemov??s knowledge based reasoning approach to game theory, (KBR), [4, 5]. Epistemic states of players are represented explicitly and reasoned about formally. We give a detailed analysis of the Centipede game using both proof theoretic and semantic machinery. This helps make the case that PDL + E can be a useful basis for the logical investigation of game theory.     

The Ineliminability of Epistemic Rationality*

Many writers have recently urged that the epistemic rationality of beliefs can depend on broadly pragmatic (as opposed to truth-directed) factors. Taken to an extreme, this line of thought leads to a view on which there is no such thing as a distinctive epistemic form of rationality. A series of papers by Susanna Rinard develops the view that something like our traditional notion of pragmatic rationality is all that is needed to account for the rationality of beliefs. This approach has undeniable attractions. But examining different versions of the approach uncovers problems. The problems help reveal why epistemic rationality is an indispensable part of understanding rationality—not only of beliefs, but of actions. We may or may not end up wanting to make a place, in our theories of epistemic rationality, for factors such as the practical or moral consequences of having beliefs. But a purely pragmatic notion of rationality—one that’s stripped of any component of distinctively epistemic evaluation—cannot do all the work that we need done.     

Reflection and Disagreement

How should you take into account the opinions of an advisor? When you completely defer to the advisor's judgment (the manner in which she responds to her evidence), then you should treat the advisor as a guru. Roughly, that means you should believe what you expect she would believe, if supplied with your extra evidence. When the advisor is your own future self, the resulting principle amounts to a version of the Reflection Principle—a version amended to handle cases of information loss. When you count an advisor as an epistemic peer, you should give her conclusions the same weight as your own. Denying that view—call it the “equal weight view”—leads to absurdity: the absurdity that you could reasonably come to believe yourself to be an epistemic superior to an advisor simply by noting cases of disagreement with her, and taking it that she made most of the mistakes. Accepting the view seems to lead to another absurdity: that one should suspend judgment about everything that one's smart and well‐informed friends disagree on, which means suspending judgment about almost everything interesting. But despite appearances, the equal weight view does not have this absurd consequence. Furthermore, the view can be generalized to handle cases involving not just epistemic peers, but also epistemic superiors and inferiors.     

Automatic verification of multi-agent systems by model checking via ordered binary decision diagrams

We present a methodology for the verification of multi-agent systems, whose properties are specified by means of a modal logic that includes a temporal, an epistemic, and a modal operator to reason about correct behaviour of agents. The verification technique relies on model checking via ordered binary decision diagrams. We present an implementation and report on experimental results for two scenarios: the bit transmission problem with faults and the protocol of the dining cryptographers.     

Wondering what might be

This paper explores the possibility of supplementing the suppositional view of indicative conditionals with a corresponding view of epistemic modals. The most striking feature of the suppositional view consists in its claim that indicative conditionals are to be evaluated by conditional probabilities. On the basis of a natural link between indicative conditionals and epistemic modals, a corresponding thesis about the probabilities of statements governed by epistemic modals can be derived. The paper proceeds by deriving further consequences of this thesis, in particular, the logic of epistemic modals and their logical interaction with indicative conditionals are studied.     

Unconfirmed peers and spinelessness

The Equal Weight View holds that, when we discover we disagree with an epistemic peer, we should give our peer’s judgment as much weight as our own. But how should we respond when we cannot tell whether those who disagree with us are our epistemic peers? I argue for a position I will call the Earn-a-Spine View. According to this view, parties to a disagreement can remain confident, at least in some situations, by finding justifiable reasons to think their opponents are less credible than themselves, even if those reasons are justifiable only because they lack information about their opponents.     

Relies to our critics

We respond to the central concerns raised by our commentators to our book, The Epistemological Spectrum. Casullo believes that our account of what we term “low-grade a priori” justification provides important clarification of a kind of philosophical reflection. However he objects to calling such reflection a priori. We explain what we think is at stake. Along the way, we comment on his idea of that there may be an epistemic payoff to making a distinction between assumptions and presumptions. In the book, we argued that an epistemically important form of nonaccidental reliability can be understood as a matter of processes being “transglobally reliable under modulational control.” Graham recommends another form of nonaccidental reliability, one rooted in evolutionary etiology. We explain why we think that the reliability of perceptual processes is best understood as turning of the kinds of modulational control that we highlight. We clarify how this approach represents a kind of reasonable epistemic patience—modulational control takes time, as it must turn on agents generating information about their own capacities and foibles. Lyons raises interesting questions regarding how (what we term) morphological content possessed by the agent can do the work that we set for it. We argue that it is necessary in order for agents to accommodate the background information that is relevant to many central problems of belief formation. We clarify how it can be expected to work.     

The virtues of epistemic conservatism

Although several important methodologies implicitly assume the truth of epistemic conservatism, the view that holding a belief confers some measure of justification on the belief, recent criticisms have led some to conclude that epistemic conservatism is an implausible view. That conclusion is mistaken. In this article, I propose a new formulation of epistemic conservatism that is not susceptible to the criticisms leveled at earlier formulations of epistemic conservatism. In addition to withstanding these criticisms, this formulation of epistemic conservatism has several benefits. First, this formulation has the benefits of earlier formulations of epistemic conservatism, that is to say it makes sense of our intuitions about justification in regard to both memory beliefs and beliefs for which we have forgotten our evidence. Second, it provides a good way of responding to the skeptic’s challenge concerning the possibility of possessing knowledge of the external world posed by the Alternative Hypotheses argument. Third, it provides responses to both forms of a new skeptical problem plaguing basic knowledge structure theories, the Problem of Easy Knowledge formulated by Stewart Cohen. I argue that given the many benefits of this formulation of epistemic conservatism and the fact that it is not vulnerable to the criticisms that undermine earlier formulations of epistemic conservatism, this formulation of epistemic conservatism is a plausible view to maintain.