The Knower Paradox has had a brief but eventful history, and principles of epistemic closure (which say that a subject automatically knows any proposition she knows to be materially implied, or logically entailed, by a proposition she already knows) have been the subject of tremendous debate in epistemic logic and epistemology more generally, especially because the fate of standard arguments for and against skepticism seems to turn on the fate of closure. As far as I can tell, however, no one (...) working in either area has emphasized the result I emphasize in this paper: the Knower Paradox just falsifies even the most widely accepted general principles of epistemic closure. After establishing that result, I discuss five of its more important consequences. (shrink)

Moore's paradox arises from the logicaloddity of sentences of the form`P and I do not believe that P'or `P and I believe that not-P'. Thiskind of sentence is logically peculiarbecause it is absurd to assert it, although it isnot a logical contradiction. In this paperI offer a new proposal. I argue that Moore's paradox arises because there is a defaultprocedure for evaluating a self-ascribed belief sentence and one is presumptivelyjustified in believing that one believes a sentence when one sincerely assents (...) to it. (shrink)

In this paper we will show that Hempel's covering law model can't deal very well with explanations that are based on incomplete knowledge. In particular the symmetry thesis, which is an important aspect of the covering law model, turns out to be problematic for these explanations. We will discuss an example of an electric circuit, which clearly indicates that the symmetry of explanation and prediction does not always hold. It will be argued that an alternative logic for causal explanation is (...) needed. And we will investigate to what extent non-monotonic epistemic logic can provide such an alternative logical framework. Finally we will show that our non-monotonic logical analysis of explanation is not only suitable for simple cases such as the electric circuit, but that it also sheds new light on more controversial causal explanations such as Milton Friedman's explanation of the business cycle. (shrink)

Theories of causation may imply that your birth causes your death, which seems odd in the way that it is not odd to say that your birth precedes your death. Theories of knowledge may imply that the object of knowledge is the same as the object of belief, although we know but do not believe facts and we can know a proposition without knowing whether it is true.

The purpose of this paper is to work toward an explicit logic and semantics for a game theoretically inspired theory of action. The purpose of the logic is to explicate the conceptual machinery implicit in the dialogue-game model of rational discourse developed in Carlson (1983).A variety of ideas and techniques of modal and philosophical logic are used to define a model structure that generalizes the game theoretical notion of a game in extensive form (von Neumann and Morgenstern, 1944). Relative to (...) this model structure, semantic characterizations are given to the action-theoretic notions oftime, possibility, belief, preference, ability, intention, action, andrationality. The unification of these characterizations under the game-theoretical paradigm leads to insights about the logical interdependences between these concepts. (shrink)

In discussion of the "Principle of Identity" in the Treatise Hume presents a puzzle about identity - not a puzzle for semantics, like Frege's, but a puzzle for a theory of representation. In this essay I am less concerned with issues of Hume interpretation and more concerned with the puzzle itself.

This paper defends a cognitive-motivational account of intending against recent criticism by J. Garcia, connects intending with a number of other concepts important in the theory of action — including decison, volition, and planning — and explores some principles of intention transfer construed as counterparts of epistemic principles governing closure for belief and justification. Several routes to intention formation are described; the role of intentions in planning is examined; and a holistic conception of intention formation and change is stressed. The (...) proposed conception of intending as embodying at once a cognitive and a motivational commitment to action is thus shown to help in understanding both the explanation of action and the rationality of agents. (shrink)

I argue that Moore's propositions, for example, 'I went to the pictures last Tuesday but I don't believe that I did' cannot be rationally believed. Their assertors either cannot be rationally believed or cannot be believed to be rational. This analysis is extended to Moorean propositions such as God knows that I am an atheist and I believe that this proposition is false. I then defend the following definition of assertion: anyone asserts that p iff that person expresses a belief (...) that p with the intention of causing relevant epistemic change in the cognition of an actual or potential audience. (shrink)

Many formalisms for reasoning about knowing commit an agent to be logically omniscient. Logical omniscience is an unrealistic principle for us to use to build a real-world agent, since it commits the agent to knowing infinitely many things. A number of formalizations of knowledge have been developed that do not ascribe logical omniscience to agents. With few exceptions, these approaches are modifications of the possible-worlds semantics. In this paper we use a combination of several general techniques for building non-omniscient reasoners. (...) First we provide for the explicit representation of notions such as problems, solutions, and problem solving activities, notions which are usually left implicit in the discussions of autonomous agents. A second technique is to take explicitly into account the notion of resource when we formalize reasoning principles. We use the notion of resource to describe interesting principles of reasoning that are used for ascribing knowledge to agents. For us, resources are abstract objects. We make extensive use of ordering and inaccessibility relations on resources, but we do not find it necessary to define a metric. Using principles about resources without using a metric is one of the strengths of our approach.We describe the architecture of a reasoner, built from a finite number of components, who solves a puzzle, involving reasoning about knowing, by explicitly using the notion of resource. Our approach allows the use of axioms about belief ordinarily used in problem solving – such as axiom K of modal logic – without being forced to attribute logical omniscience to any agent. In particular we address the issue of how we can use resource-unbounded (e.g., logically omniscient) reasoning to attribute knowledge to others without introducing contradictions. We do this by showing how omniscient reasoning can be introduced as a conservative extension over resource-bounded reasoning. (shrink)

In this paper, the traditional view that argumentum ad ignorantiam is a logical fallacy is challenged, and lessons are drawn on how to model inferences drawn from knowledge in combination with ones drawn from lack of knowledge. Five defeasible rules for evaluating knowledge-based arguments that apply to inferences drawn under conditions of lack of knowledge are formulated. They are the veridicality rule, the consistency of knowledge rule, the closure of knowledge rule, the rule of refutation and the rule for argument (...) from ignorance. The basic thesis of the paper is that knowledge-based arguments, including the argument from ignorance, need to be evaluated by criteria for epistemic closure and other evidential rules that are pragmatic in nature, that need to be formulated and applied differently at different stages of an investigation or discussion. The paper helps us to understand practical criteria that should be used to evaluate all arguments based on knowledge and/or ignorance. (shrink)

In an information state where various agents have both factual knowledge and knowledge about each other, announcements can be made that change the state of information. Such informative announcements can have the curious property that they become false because they are announced. The most typical example of that is 'fact p is true and you don't know that', after which you know that p, which entails the negation of the announcement formula. The announcement of such a formula in a given (...) information state is called an unsuccessful update. A successful formula is a formula that always becomes common knowledge after being announced. Analysis of information systems and 'philosophical puzzles' reveals a growing number of dynamic phenomena that can be described or explained by unsuccessful updates. This increases our understanding of such philosophical problems. We also investigate the syntactic characterization of the successful formulas. (shrink)

Sound and complete axiomatizations are provided for a number of different logics involving modalities for the knowledge of multiple agents and operators for branching time, extending previous work of Halpern, van der Meyden and Vardi [to appear, SIAM Journal on Computing] for logics of knowledge and linear time. The paper considers the system constraints of synchrony, perfect recall and unique initial states, which give rise to interaction axioms. The language is based on the temporal logic CTL*, interpreted with respect to (...) a version of the bundle semantics. (shrink)

Positive thinkers love Watty Piper's The little engine that could. The story features a train laden with toys for deserving children on the other side of the mountain. After the locomotive breaks down, a sequence of snooty locomotives come up the track. Each engine refuses to pull the train up the mountain. They are followed by a weary old locomotive that declines, saying "I cannot. I cannot. I cannot." But then a bright blue engine comes up the track. He manages (...) to chug over the mountain by averring "I think I can. I think I can. I think can.". (shrink)

A century ago, Charles S. Peirce proposed a logical approach to modalities that came close to possible-worlds semantics. This paper investigates his views on modalities through his diagrammatic logic of Existential Graphs (EGs). The contribution of the gamma part of EGs to the study of modalities is examined. Some ramifications of Peirce’s remarks are presented and placed into a contemporary perspective. An appendix is included that provides a transcription with commentary of Peirce’s unpublished manuscript on modality from 1901.

Awareness logic is a type of belief logic in which an agent's beliefs are restricted to those sentences that the agent is aware of. Awareness logic is a successful way to circumvent the problem of omniscience so that actual belief is modelled in a reasonable way. In this paper, we suggest a new method modelling awareness and actual belief by using two-dimensional logics. We show that the two-dimensional logics are flexible tools. Different types of concepts of awareness can be easily (...) modelled by this method. (shrink)

Two approaches for defining common knowledge coexist in the literature: the infinite iteration definition and the circular or fixed point one. In particular, an original modelization of the fixed point definition was proposed by Barwise in the context of a non-well-founded set theory and the infinite iteration approach has been technically analyzed within multi-modal epistemic logic using neighbourhood semantics by Lismont. This paper exhibits a relation between these two ways of modelling common knowledge which seem at first quite different.

The purpose of this survey is twofold: (1) to place some centralthemes of epistemic logic in a general epistemological context,and (2) to outline a new framework for epistemic logic developedjointly with S. Andur Pedersen unifying some key ``mainstream''epistemological concerns with the ``formal'' epistemologicalapparatus.

This paper consists of two main parts and a coda. In the first part I present the ''binding theory'' of presupposition projection, which is the framework that I adopt in this paper (Section 1.1). I outline the main problems that arise in the interplay between presuppositions and anaphors on the one hand and attitude reports on the other (Section 1.2), and discuss Heim''s theory of presuppositions in attitude contexts (Section 1.3).In the second part of the paper I present my own (...) proposal. To begin with, I define an extension of DRT in which attitude reports can be represented (Sections 2.1–2.2). I then argue that the verb believe triggers a certain presupposition and that, given the binding theory, this presupposition determines the projection behaviour of the verb (Section 2.3). This analysis yields predictions which are incomplete in the sense that they do not fully account for speakers'' intuitions about presuppositions and anaphors in belief contexts. In Section 2.4 I suggest that this is as it should be because we may assume on independent grounds that there is a class of plausibility inferences which complement the predictions of the presupposition theory. Finally, the analysis is extended to the verb want (Section 2.5). (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)

This paper examines the paradox of revisability. This paradox was proposed by Jerrold Katz as a problem for Quinean naturalised epistemology. Katz employs diagonalisation to demonstrate what he takes to be an inconsistency in the constitutive principles of Quine's epistemology. Specifically, the problem seems to rest with the principle of universal revisability which states that no statement is immune to revision. In this paper it is argued that although there is something odd about employing universal revisability to revise itself, there (...) is nothing paradoxical about this. At least, there is no paradox along the lines suggested by Katz. (shrink)

We present a framework for intensional reasoning in typed -calculus. In this family of calculi, called Modal Pure Type Systems (MPTSs), a propositions-as-types-interpretation can be given for normal modal logics. MPTSs are an extension of the Pure Type Systems (PTSs) of Barendregt (1992). We show that they retain the desirable meta-theoretical properties of PTSs, and briefly discuss applications in the area of knowledge representation.

I hope I have convinced the reader that DR theory offers at least some exciting potential when applied to the semantics of belief reports. It differs considerably from other approaches, and it makes intuitively acceptable predictions that other theories do not. The theory also provides a novel approach to the semantics of other propsitional attitude reports. Further, DR theory enables one to approach the topic of anaphora within belief and other propositional attitude contexts in a novel way, thus combining the (...) semantics developed here with one of the theory's original motivations (Kamp, 1981a). However, these are unfortunately topics that I must reserve for another time. (shrink)

Some practical criteria for free-will are suggested where free-will is a matter of degree. It is argued that these are more appropriate than some extremely idealised conceptions. Thus although the paper takes lessons from philosophy it avoids idealistic approaches as irrelevant. A mechanism for allowing an agent to meet these criteria is suggested: that of facilitating the gradual emergence of free-will in the brain via an internal evolutionary process. This meets the requirement that not only must the choice of action (...) be free but also choice in the method of choice, and choice in the method of choice of the method of choice etc. This is directly analogous to the emergence of life from non-life. Such an emergence of indeterminism with respect to the conditions of the agent fits well with the `Machiavellian Intelligence Hypothesis' which posits that our intelligence evolved (at least partially) to enable us to deal with social complexity and modelling `arms races'. There is a clear evolutionary advantage in being internally coherent in seeking to fulfil ones goals and unpredictable by ones peers. To fully achieve this vision several other aspects of cognition are necessary: open-ended strategy development; the meta-evolution of the evolutionary process; the facility to anticipate the results of strategies; and the situating of this process in a society of competitive peers. Finally the requirement that reports of the deliberations that lead to actions need to be socially acceptable leads to the suggestion that the language that the strategies are developed within be subject to a normative process in parallel with the development of free-will. An appendix outlines a philosophical position in support of my position. (shrink)

ABSTRACT First, I consider a few motivations to idealize epistemic logics1 in such a degree that brings up the problem of logical omniscience [LOP]. I argue that the main motivation to hold omniscience is of a philosophical-scientific2 background, in the sense philosophers have a not so peculiar way of investigating underlying mechanisms, i.e., the interaction of several different components of complex systems may be better understood in isolation, even if such components are not found isolated in a realistic context. It (...) is defended that the implicit and explicit knowledge distinction is compatible that view since idealizations made by modal epistemic logic are so strong that the agents they describe hardly have anything in common with real agents. I conclude by showing how LOP can be accommodated in the logic of being informed using the Inverse Relationship Principle. 1Epistemic modal logics and the logic of being informed may collapse in many scenarios, as shown in previous articles. 2Does not necessarily imply in a naturalized epistemology a la. For a plea for non-naturalism as constructionism see. (shrink)

In this paper, we propose a decidable single-agent modal logic for reasoning about goal-directed “knowing how”, based on ideas from linguistics, philosophy, modal logic, and automated planning in AI. We first define a modal language to express “I know how to guarantee \ given \” with a semantics based not on standard epistemic models but on labeled transition systems that represent the agent’s knowledge of his own abilities. The semantics is inspired by conformant planning in AI. A sound and complete (...) proof system is given to capture valid reasoning patterns, which highlights the compositional nature of “knowing how”. The logical language is further extended to handle knowing how to achieve a goal while maintaining other conditions. (shrink)

This paper argues that questions have an important role to to play in logic, both semantically and proof-theoretically. Semantically, we show that by generalizing the classical notion of entailment to questions, we can capture not only the standard relation of logical consequence, which holds between pieces of information, but also the relation of logical dependency, which holds between information types. Proof-theoretically, we show that questions may be used in inferences as placeholders for arbitrary information of a given type; by manipulating (...) such placeholders, we may construct formal proofs of dependencies. Finally, we show that such proofs have a specific kind of constructive content: they do not just witness the existence of a certain dependency, but actually encode a method for transforming information of the types described by the assumptions into information of the type described by the conclusion. (shrink)

Nelson Goodman cast the ‘problem of induction’ as the task of articulating the principles and standards by which to distinguish valid from invalid inductive inferences. This paper explores some logical bounds on the ability of a rational reasoner to accomplish this task. By a simple argument, either an inductive inference method cannot admit its own fallibility, or there exists some non-inferable hypothesis whose non-inferability the method cannot infer (violating the principle of ‘negative introspection’). The paper discusses some implications of this (...) limited self-knowledge for the justifiability of inductive inferences, auto-epistemic logic, and the epistemic foundations of game theory. (shrink)

Any contextualist approach to knowledge has to provide a plausible definition of the concept of context and spell out the mechanisms of context changes. Since it is the dynamics of context change that carry the main weight of the contextualist position, not every mechanism will be capable of filling that role. In particular, I argue that one class of mechanisms that is most popularly held to account for context changes, namely those that arise out of shifts of conversational parameters in (...) discourses involving knowledge claims, are not suited to the job because they cannot account for the genuinely epistemic nature of the context shift. A form of epistemic contextualism that defines the context through the structure of our epistemic projects is suggested. Context changes in this account are linked to changes in the background assumptions operative in our epistemic projects and the methods used to carry out our inquiries. (shrink)

Purpose: The paper discusses the concept of a reflexive domain, an arena where the apparent objects as entities of the domain are actually processes and transformations of the domain as a whole. Human actions in the world partake of the patterns of reflexivity, and the productions of human beings, including science and mathematics, can be seen in this light. Methodology: Simple mathematical models are used to make conceptual points. Context: The paper begins with a review of the author's previous work (...) on eigenforms - objects as tokens for eigenbehaviors, the study of recursions and fixed points of recursions. The paper also studies eigenforms in the Boolean reflexive models of Vladimir Lefebvre. Findings: The paper gives a mathematical definition of a reflexive domain and proves that every transformation of such a domain has a fixed point. Thus eigenforms exist in reflexive domains. We discuss a related concept called a "magma." A magma is composed entirely of its own structure-preserving transformations. Thus a magma can be regarded as a model of reflexivity and we call a magma "reflexive" if it encompasses all of its structure-preserving transformations. We prove a fixed point theorem for reflexive magmas. We then show how magmas are related to knot theory and to an extension of set theory using knot diagrammatic topology. This work brings formalisms for self- reference into a wider arena of process algebra, combinatorics, non-standard set theory and topology. The paper then discusses how these findings are related to lambda calculus, set theory and models for self- reference. The last section of the paper is an account of a computer experiment with a variant of the Life cellular automaton of John H. Conway. In this variant, 7-Life, the recursions lead to self-sustaining processes with very long evolutionary patterns. We show how examples of novel phenomena arise in these patterns over the course of large time scales. Value: The paper provides a wider context and mathematical conceptual tools for the cybernetic study of reflexivity and circularity in systems. (shrink)

A propositional logic of explicit proofs, LP, was introduced in [S. Artemov, Explicit provability and constructive semantics, The Bulletin for Symbolic Logic 7 1–36], completing a project begun long ago by Gödel, [K. Gödel, Vortrag bei Zilsel, translated as Lecture at Zilsel’s in: S. Feferman , Kurt Gödel Collected Works III, 1938, pp. 62–113]. In fact, LP can be looked at in a more general way, as a logic of explicit evidence, and there have been several papers along these lines. (...) A major result about LP is the Realization Theorem, that says any theorem of S4 can be converted into a theorem of LP by some replacement of necessitation symbols with explicit proof terms. Thus the necessitation operator of S4 can be seen as a kind of implicit existential quantifier: there exists a proof term such that…. In this paper, quantification over evidence is introduced into LP, and it is shown that the connection between S4 necessitation and the existential quantifier becomes an explicit one. The extension of LP with quantifiers is called QLP. A semantics and an axiom system for QLP are given, soundness and completeness are established, and several results are proved relating QLP to LP and to S4. (shrink)

This paper discusses the possibility of modelling inductive inference (Gold 1967) in dynamic epistemic logic (see e.g. van Ditmarsch et al. 2007). The general purpose is to propose a semantic basis for designing a modal logic for learning in the limit. First, we analyze a variety of epistemological notions involved in identification in the limit and match it with traditional epistemic and doxastic logic approaches. Then, we provide a comparison of learning by erasing (Lange et al. 1996) and iterated epistemic (...) update (Baltag and Moss 2004) as analyzed in dynamic epistemic logic. We show that finite identification can be modelled in dynamic epistemic logic, and that the elimination process of learning by erasing can be seen as iterated belief-revision modelled in dynamic doxastic logic. Finally, we propose viewing hypothesis spaces as temporal frames and discuss possible advantages of that perspective. (shrink)

What is the minimal algebraic structure to reason about information flow? Do we really need the full power of Boolean algebras with co-closure and de Morgan dual operators? How much can we weaken and still be able to reason about multi-agent scenarios in a tidy compositional way? This paper provides some answers.