We need to understand the impossible. Francesco Berto and Mark Jago start by considering what the concepts of meaning, information, knowledge, belief, fiction, conditionality, and counterfactual supposition have in common. They are all concepts which divide the world up more finely than logic does. Logically equivalent sentences may carry different meanings and information and may differ in how they're believed. Fictions can be inconsistent yet meaningful. We can suppose impossible things without collapsing into total incoherence. Yet for the leading philosophical (...) theories of meaning, these phenomena are an unfathomable mystery. To understand these concepts, we need a metaphysical, logical, and conceptual grasp of situations that could not possibly exist: Impossible Worlds. This book discusses the metaphysics of impossible worlds and applies the concept to a range of central topics and open issues in logic, semantics, and philosophy. It considers problems in the logic of knowledge, the meaning of alternative logics, models of imagination and mental simulation, the theory of information, truth in fiction, the meaning of conditional statements, and reasoning about the impossible. In all these cases, impossible worlds have an essential role to play. (shrink)

The concept of knowledge can be modelled in epistemic modal logic and, if modelled by using a standard modal operator, it is subject to the problem of logical omniscience. The classical solution to this problem is to distinguish between implicit and explicit knowledge and to construe the knowledge operator as capturing the concept of implicit knowledge. In addition, since a proposition is said to be implicitly known just in case it is derivable from the set of propositions that are explicitly (...) known by using a certain set of logical rules, the concept of implicit knowledge is definable on the basis of the concept of explicit knowledge. In any case, both implicit and explicit knowledge are typically characterized as factive, i.e. such that it is always the case that what is known is also true. The aim of the present paper is twofold: first, we will develop a dynamic system of explicit intersubjective knowledge that allows us to introduce the operator of implicit knowledge by definition; secondly, we will show that it is not possible to hold together the following two theses: (1) the concept of implicit knowledge is definable along the lines indicated above and (2) the concept of implicit knowledge is factive. (shrink)

This chapter presents a new semantics for inductive empirical knowledge. The epistemic agent is represented concretely as a learner who processes new inputs through time and who forms new beliefs from those inputs by means of a concrete, computable learning program. The agent’s belief state is represented hyper-intensionally as a set of time-indexed sentences. Knowledge is interpreted as avoidance of error in the limit and as having converged to true belief from the present time onward. Familiar topics are re-examined within (...) the semantics, such as inductive skepticism, the logic of discovery, Duhem’s problem, the articulation of theories by auxiliary hypotheses, the role of serendipity in scientific knowledge, Fitch’s paradox, deductive closure of knowability, whether one can know inductively that one knows inductively, whether one can know inductively that one does not know inductively, and whether expert instruction can spread common inductive knowledge—as opposed to mere, true belief—through a community of gullible pupils. (shrink)

We present a framework for verifying systems composed of heterogeneous reasoning agents, in which each agent may have differing knowledge and inferential capabilities, and where the resources each agent is prepared to commit to a goal (time, memory and communication bandwidth) are bounded. The framework allows us to investigate, for example, whether a goal can be achieved if a particular agent, perhaps possessing key information or inferential capabilities, is unable (or unwilling) to contribute more than a given portion of its (...) available computational resources or bandwidth to the problem. We present a novel temporal epistemic logic, BMCL-CTL , which allows us to describe a set of reasoning agents with bounds on time, memory and the number of messages they can exchange. The bounds on memory and communication are expressed as axioms in the logic. As an example, we show how to axiomatise a system of agents which reason using resolution and prove that the resulting logic is sound and complete. We then show how to encode a simple system of reasoning agents specified in BMCL-CTL in the description language of the Mocha model checker (Alur et al., Proceedings of the tenth international conference on computer-aided verification (CAV) , 1998), and verify that the agents can achieve a goal only if they are prepared to commit certain time, memory and communication resources. (shrink)

Syntactic logics do not suffer from the problems of logical omniscience but are often thought to lack interesting properties relating to epistemic notions. By focusing on the case of rule-based agents, I develop a framework for modelling resource-bounded agents and show that the resulting models have a number of interesting properties.

The logical omniscience problem, whereby standard models of epistemic logic treat an agent as believing all consequences of its beliefs and knowing whatever follows from what else it knows, has received plenty of attention in the literature. But many attempted solutions focus on a fairly narrow specification of the problem: avoiding the closure of belief or knowledge, rather than showing how the proposed logic is of philosophical interest or of use in computer science or artificial intelligence. Sentential epistemic logics, as (...) opposed to traditional possible worlds approaches, do not suffer from the problems of logical omniscience but are often thought to lack interesting epistemic properties. In this paper, I focus on the case of rule-based agents, which play a key role in contemporary AI research but have been neglected in the logical literature. I develop a framework for modelling monotonic, nonmonotonic and introspective rule-based reasoners which have limited cognitive resources and prove that the resulting models have a number of interesting properties. An axiomatization of the resulting logic is given, together with completeness, decidability and complexity results. (shrink)

Reasoning about mental states and processes is important in various subareas of the legal domain. A trial lawyer might need to reason and the beliefs, reasoning and other mental states and processes of members of a jury; a police officer might need to reason about the conjectured beliefs and reasoning of perpetrators; a judge may need to consider a defendant's mental states and processes for the purposes of sentencing and so on. Further, the mental states in question may themselves be (...) about the mental states and processes of other people. Therefore, if AI systems are to assist with reasoning tasks in law, they may need to be able to reason about mental states and processes. Such reasoning is riddled with uncertainty, and this is true in particular in the legal domain. The article discusses how various different types of uncertainty arise, and shows how they greatly complicate the task of reasoning about mental states and processes. The article concentrates on the special case of states of belief and processes of reasoning, and sketches an implemented, prototype computer program (ATT-Meta) that copes with the various types of uncertainty in reasoning about beliefs and reasoning. In particular, the article outlines the system's facilities for handling conflict between different lines of argument, especially when these lie within the reasoning of different people. The system's approach is illustrated by application to a real-life mugging example. [NB: The date on the archived preprint avail via this Phil* page has an incorrect date, 2011, on it. The correct date is 2001.]. (shrink)

The intentional stance is the strategy of prediction and explanation that attributes beliefs, desires, and other states to systems and predicts future behavior from what it would be rational for an agent to do, given those beliefs and desires. Any system whose performance can be thus predicted and explained is an intentional system, whatever its innards. The strategy of treating parts of the world as intentional systems is the foundation of but is also exploited in artificial intelligence and cognitive science (...) more generally, as well as in evolutionary theory. An analysis of the role of the intentional stance and its presuppositions supports a naturalistic theory of mental states and events, their content or intentionality, and the relation between levels of explanation and neurophysiological or mechanistic levels of explanation. As such, the analysis of the intentional stance grounds a theory of the mind and its relation to the body. (shrink)

In this paper, I defend the metalinguistic solution to the problem of mathematical omniscience for the possible-worlds account of propositions by combining it with a computational model of knowledge and belief. The metalinguistic solution states that the objects of belief and ignorance in mathematics are relations between mathematical sentences and what they express. The most pressing problem for the metalinguistic strategy is that it still ascribes too much mathematical knowledge under the standard possible-worlds model of knowledge and belief on which (...) these are closed under entailment. I first argue that Stalnaker's fragmentation strategy is insufficient to solve this problem. I then develop an alternative, computational strategy: I propose a model of mathematical knowledge and belief adapted from the algorithmic model of Halpern et al. which, when combined with the metalinguistic strategy, entails that mathematical knowledge and belief require computational abilities to access metalinguistic information, and thus aren't closed under entailment. As I explain, the computational model generalizes beyond mathematics to a version of the functionalist theory of knowledge and belief that motivates the possible-worlds account in the first place. I conclude that the metalinguistic and computational strategies yield an attractive functionalist, possible-worlds account of mathematical content, knowledge, and inquiry. (shrink)

This paper is about the alethic aspect of epistemic rationality. The most common approaches to this aspect are either normative (what a reasoner ought to/may believe?) or evaluative (how rational is a reasoner?), where the evaluative approaches are usually comparative (one reasoner is assessed compared to another). These approaches often present problems with blindspots. For example, ought a reasoner to believe a currently true blindspot? Is she permitted to? Consequently, these approaches often fail in describing a situation of alethic maximality, (...) where a reasoner fulfills all the alethic norms and could be used as a standard of rationality (as they are, in fact, used in some of these approaches). I propose a function α, which accepts a set of beliefs as inputand returns a numeric alethic value. Then I use this function to define a notion of alethic maximality that is satisfiable by finite reasoners (reasoners with cognitive limitations) and does not present problems with blindspots. Function α may also be used in alethic norms and evaluation methods (comparative and non-comparative) that may be applied to finite reasoners and do not present problems with blindspots. A result of this investigation isthat the project of providing purely alethic norms is defective. The use of function α also sheds light on important epistemological issues, such as the lottery and the preface paradoxes, and the principles of clutter avoidance and reflection. (shrink)

The most widespread models of rational reasoners (the model based on modal epistemic logic and the model based on probability theory) exhibit the problem of logical omniscience. The most common strategy for avoiding this problem is to interpret the models as describing the explicit beliefs of an ideal reasoner, but only the implicit beliefs of a real reasoner. I argue that this strategy faces serious normative issues. In this paper, I present the more fundamental problem of logical omnipotence, which highlights (...) the normative content of the problem of logical omniscience. I introduce two developments of the notion of implicit belief (accessible and stable belief ) and use them in two versions of the most common strategy applied to the problem of logical omnipotence. (shrink)

We propose a solution to the problem of logical omniscience in what we take to be its fundamental version: as concerning arbitrary agents and the knowledge attitude per se. Our logic of knowledge is a spin-off from a general theory of thick content, whereby the content of a sentence has two components: an intension, taking care of truth conditions; and a topic, taking care of subject matter. We present a list of plausible logical validities and invalidities for the logic of (...) knowledge per se for arbitrary agents, and isolate three explanatory factors for them: the topic-sensitivity of content; the fragmentation of knowledge states; the defeasibility of knowledge acquisition. We then present a novel dynamic epistemic logic that yields precisely the desired validities and invalidities, for which we provide expressivity and completeness results. We contrast this with related systems and address possible objections. (shrink)

This paper proposes a new account of bounded or minimal doxastic rationality (in the sense of Cherniak 1986), based on the notion that beliefs are answers to questions (à la Yalcin 2018). The core idea is that minimally rational beliefs are linked through thematic connections, rather than entailment relations. Consequently, such beliefs are not deductively closed, but they are closed under parthood (where a part is an entailment that answers a smaller question). And instead of avoiding all inconsistency, minimally rational (...) believers only avoid blatant inconsistencies (where some beliefs are blatantly inconsistent when they contradict one another on a particular question). Rather than cohering into a single overall world view, beliefs are more loosely connected in what is best described as a web of questions. This view of minimally rational belief naturally gives rise to an account of deductive inquiry on which deductive reasoning is a matter of posing new questions. (shrink)

Herbrand’s theorem is a central fact about classical logic, [9, 10]. It provides a constructive method for associating, with each first-order formula X, a sequence of formulas X1, X2, X3, . . . , so that X has a first-order proof if and only if some Xi is a tautology. Herbrand’s theorem serves as a constructive alternative to..

We propose a framework for modelling situated resource-bounded agents. The framework is based on an objective ascription of intentional modalities and can be easily tailored to the system we want to model and the properties we wish to specify. As an elaboration of the framework, we introduce a logic, OBA, for describing the observations, beliefs, goals and actions of simple agents, and show that OBA is complete, decidable and has an efficient model checking procedure, allowing properties of agents specified in (...) OBA to be verified using standard theorem proving or model checking techniques. (shrink)

The propositional content of a reference is the proposition attributing to the referent the properties that correspond to the nouns and modifiers in the reference (for example, the propositional content of `Mary' is that the referent is named`Mary'). During language comprehension, the hearer or reader must determine the set of beliefs with respect to which the propositional content of a reference is to be understood. In the prototypical case, this set consists of the propositions that she believes that the speaker (...) or writer believes that she and the speaker or writer mutually believe. This paper identifies two contexts in which the propositional content of a specific reference is not understood with respect to this set--subjective and objective sentences in third-person fictional narrative text--and identifies some implications of this for understanding specific references in these contexts. (shrink)

We introduce a methodology whereby an arbitrary logic system L can be enriched with temporal features to create a new system T(L). The new system is constructed by combining L with a pure propositional temporal logic T (such as linear temporal logic with Since and Until) in a special way. We refer to this method as adding a temporal dimension to L or just temporalising L. We show that the logic system T(L) preserves several properties of the original temporal logic (...) like soundness, completeness, decidability, conservativeness and separation over linear flows of time. We then focus on the temporalisation of first-order logic, and a comparison is make with other first-order approaches to the handling of time. (shrink)

Konolige''s technical notion of belief based on deduction structures is briefly reviewed and its usefulness for the design of artificial agents with limited representational and deductive capacities is pointed out. The design of artificial agents with more sophisticated representational and deductive capacities is then taken into account. Extended representational capacities require in the first place a solution to the intensional context problems. As an alternative to Konolige''s modal first-order language, an approach based on type-free property theory is proposed. It considers (...) often neglected issues, such as the need for a more general account of thede dicto-de re distinction, and quasi-indicators. Extended deductive capacities require a subdivision of Konolige''s notion of belief into two distinct technical notions,potential anddispositional belief. The former has to do with what an artificial agent could in principle come to actively believe, given enough time and its specific logical competence; the latter with what an agent can be assumed to believe with respect to a specific goal to be fulfilled. (shrink)

The process of rationally revising beliefs in the light of new information is a topic of great importance and long-standing interest in artificial intelligence. Moreover, significant progress has been made in understanding the philosophical, logical, and computational foundations of belief revision. However, very little research has been reported with respect to the revision of other mental states, most notably propositional attitudes such as desires and intentions. In this paper, we present a first attempt to formulate a general framework for understanding (...) the revision of mental states. We develop an abstract belief-desire-intention model of agents, and introduce a notion of rationality for this model. We then present a series of formal postulates characterizing the processes of adding beliefs, desires, and intentions, updating costs and values, and removing beliefs, desires, and intentions. We also investigate the computational complexity of several problems involving the abstract model and comment on algorithms for revision. (shrink)

ABSTRACT We introduce a two-dimensional temporal logic as a formalism which enables the description of both the history of a world and the evolution of an observer's views about the history. We apply such formalism to the description of certain problems that occur in historical database systems due to updates. The historical dimension describes the history of a world according to an observer's view at a certain moment in time. The transaction dimension describes the evolution of an observer's view; changes (...) can occur in the observer's view of the present and future as well as in his views of the past. The database is seens as an observer of the history of the world. Besides describing the history of the world, the database system can also execute temporal specifications in the form of temporal actions. The two-dimensional formalism is used to describe the effects of updates in the execution of temporal actions. The detection of some problematic effects and its implementation are discussed. (shrink)