Epistemic Logic

We explore some possibilities for developing epistemic logic using truthmaker semantics. We identify three possible targets of analysis for the epistemic logician. We then list some candidate epistemic principles and review the arguments that render some controversial. We then present the classic Hintikkan approach to epistemic logic and note—as per the ‘problem of logical omniscience’—that it validates all of the aforementioned principles, controversial or otherwise. We then lay out a truthmaker framework in the style of Kit Fine and present six (...) different ways of extending this semantics with a conditional knowledge operator, drawing on notions of implication and content that are prominent in Fine’s work. We demonstrate that different logics are thereby generated, bearing on the aforementioned epistemic principles. Finally, we offer preliminary observations about the prospects for each logic. (shrink)

kk states that knowing entails knowing that one knows, and K¬K states that not knowing entails knowing that one does not know. In light of the arguments against kk and K¬K⁠, one might consider modally qualified variants of those principles. According to weak kk, knowing entails the possibility of knowing that one knows. And according to weakK¬K⁠, not knowing entails the possibility of knowing that one does not know. This paper shows that weak kk and weakK¬K are much stronger than (...) they initially appear. Jointly, they entail kk and K¬K⁠. And they are susceptible to variants of the standard arguments against kk and K¬K⁠. This has interesting implications for the debate on positive introspection and for deeper issues concerning the structure and limits of knowability. (shrink)

In this article, I cast doubt on an apparent truism, namely, that if evidence is available for gathering and use at a negligible cost, then it’s always instrumentally rational for us to gather that evidence and use it for making decisions. Call this ‘value of information’ (VOI). I show that VOI conflicts with two other plausible theses. The first is the view that an agent’s evidence can entail non-trivial propositions about the external world. The second is the view that epistemic (...) rationality requires us to update our credences by conditionalization. These two theses, given some plausible assumptions, make room for rationally biased inquiries where VOI fails. I go on to argue that this is bad news for defenders of VOI. (shrink)

We offer a general framework for theorizing about the structure of knowledge and belief in terms of the comparative normality of situations compatible with one’s evidence. The guiding idea is that, if a possibility is sufficiently less normal than one’s actual situation, then one can know that that possibility does not obtain. This explains how people can have inductive knowledge that goes beyond what is strictly entailed by their evidence. We motivate the framework by showing how it illuminates knowledge about (...) the future, knowledge of lawful regularities, knowledge about parameters measured using imperfect instruments, the connection between knowledge, belief, and probability, and the dynamics of knowledge and belief in response to new evidence. (shrink)

A fascinating recent turn in epistemology focuses on inquiring attitudes like wondering and being curious. Many have argued that these attitudes are governed by norms similar to those that govern our doxastic attitudes. Yet, to date, this work has only considered norms that might *prohibit* having certain inquiring attitudes (``norms of restriction''), while ignoring those that might *require* having them (``norms of expansion''). We aim to address that omission by offering a framework that generates norms of expansion for inquiring attitudes. (...) The framework draws on inferential erotetic logic, which we explain and augment with some theorems. We explore several of the norms that it yields - some sympathetically, others unsympathetically. (shrink)

Williamson (2000) argues that the KK principle is inconsistent with knowledge of margin for error in cases of inexact perceptual observations. This paper argues, primarily by analogy to a different scenario, that Williamson’s argument is fallacious. Margin for error principles describe the agent’s knowledge as a result of an inexact perceptual event, not the agent’s knowledge state in general. Therefore, epistemic agents can use their knowledge of margin for error at most once after a perceptual event, but not more. This (...) insight blocks a crucial step in Williamson’s original argument. Along the way, the value of standard epistemic logic for analyzing margin for error reasoning is challenged. (shrink)

This paper discusses the theoretical assumptions behind the conception of the logic of faith and deed and outlines its formal-axiomatic frame and its method of construction, which enable us to understand it as a kind of deductive science. The paper is divided into several sections, starting with the logical analysis of the ambiguous terms of ‚faith’ and ‚action’, and focusing in particular on the concepts of religious faith and deed as a type of conscious activity relating to a matter or (...) matters of social importance. After outlining the main ideas and basic assumptions of the theoretical conception of the LF&D as an axiomatic theory, the author introduces some axiom systems for: 1) the logics of faith LF, 2) the logic of deed LD, and 3) certain logics of norms DL connected with „duties” and concerning actions/deeds. Lastly, the paper outlines the scientific LF&D based on the three types of logic 1)–3). (shrink)

Tomis Kapitan’s work on Peirce’s conception of abduction was instrumental for our coming to see how Peircean abduction both relates to and is importantly different from inference to the best explanation (IBE). However, he ultimately concluded that Peirce’s conception of abduction was a muddle. Despite the deeply problematic nature of Peirce’s theory of abduction in these respects, Kapitan’s work on Peircean abduction offers insight into the nature of abductive inquiry that is importantly relevant to the task of making sense of (...) explanatory inquiry in the sciences in general. The view developed here stems from his work and involves disambiguating three forms of inference involved in Peircean abduction in terms of Reichenbach’s and Laudan’s context models of inquiry. Importantly, this includes understanding that abduction involves the context of pursuit. (shrink)

It is natural to suppose the following three: factivity of knowledge, alda-know synonymy, and the univocity of alda. However, rago-knowledge attribution, expressed by “rago alda” sentences, seems to defeat to hold them at once. In this paper, I try to dissolve this predicament, analyzing “rago alda” sentence as a kind of hybrid language expression. And the theoretical advantages, which my analysis has over other possible, alternative approaches, are to be shown.

We generalize intuitionistic tense logics to the multi-modal case by placing grammar logics on an intuitionistic footing. We provide axiomatizations for a class of base intuitionistic grammar logics as well as provide axiomatizations for extensions with combinations of seriality axioms and what we call "intuitionistic path axioms". We show that each axiomatization is sound and complete with completeness being shown via a typical canonical model construction.

In this paper I will compare two competing accounts of assertion: the knowledge account and the justified belief account. When it comes to the evidence that is typically used to assess accounts of assertion – including the evidence from lottery propositions, the evidence from Moore’s paradoxical propositions and the evidence from conversational patterns – I will argue that the justified belief account has at least as much explanatory power as its rival. I will argue, finally, that a close look at (...) the ways in which assertions can be challenged and retracted reveals a certain advantage for the justified belief account. The paper will touch upon a number of further topics along the way, including the logical interaction between knowledge and justified belief, the nature of defeat, and the hypothesis that knowledge and justified belief are normatively coincident goals. (shrink)

This paper explores the principle that knowledge is fragile, in that whenever S knows that S doesn’t know that S knows that p, S thereby fails to know p. Fragility is motivated by the infelicity of dubious assertions, utterances which assert p while acknowledging higher-order ignorance whether p. Fragility is interestingly weaker than KK, the principle that if S knows p, then S knows that S knows p. Existing theories of knowledge which deny KK by accepting a Margin for Error (...) principle can be conservatively extended with Fragility. (shrink)

One of the most intriguing claims in Sven Rosenkranz’s Justification as Ignorance is that Timothy Williamson’s celebrated anti-luminosity argument can be resisted when it comes to the condition ~K~KP—the condition that one is in no position to know that one is in no position to know P. In this paper, I critically assess this claim.

We propose a logic to reason about data collected by a num- ber of measurement systems. The semantic of this logic is grounded on the epistemic theory of measurement that gives a central role to measure- ment devices and calibration. In this perspective, the lack of evidences (in the available data) for the truth or falsehood of a proposition requires the introduction of a third truth-value (the undetermined). Moreover, the data collected by a given source are here represented by means (...) of a possible world, which provide a contextual view on the objects in the domain. We approach (possibly) conflicting data coming from different sources in a social choice theoretic fashion: we investigate viable opera- tors to aggregate data and we represent them in our logic by means of suitable (minimal) modal operators. (shrink)

Obligations can be affected by knowledge. Several approaches exist to formalize knowledge-based obligations, but no formalism has been developed yet to capture the dynamic interaction between knowledge and obligations. We introduce the dynamic extension of an existing logic for knowledge-based obligations here. We motivate the logic by analyzing several scenarios and by showing how it can capture in an original manner several fundamental deontic notions such as absolute, prima facie and all-things-considered obligations. Finally, in the dynamic epistemic logic tradition, we (...) provide reduction axioms for the dynamic operator of the new logic. (shrink)

Rosenkranz (2021) devised two bimodal epistemic logics: an idealized one and a realistic one. The former is shown to be sound with respect to a class of neighborhood frames called i-frames. Rosenkranz designed a specific i-frame able to invalidate a series of undesired formulas, proving that these are not theorems of the idealized logic. Nonetheless, an unwanted formula and an unwanted rule of inference are not invalidated. Invalidating the former guarantees the distinction between the two modal operators characteristic of the (...) logic, while invalidating the latter is crucial in order to deal with the problem of logical omniscience. In this paper, I present an i-frame able to invalidate all the undesired formulas already invalidated by Rosenkranz, together with the missing formula and rule of inference. (shrink)

In this article, I propose a formal criterion that distinguishes between deductively valid arguments that do and do not beg the question. I define the concept of a Never-failing Minimally Competent Knower (NMCK) and suggest that an argument begs the question just in case it cannot possibly assist an NMCK in extending his or her knowledge.

There is a very plausible principle linking abilities and possibilities: If S is able to Φ, then it is metaphysically possible that S Φ’s. Jack Spencer recently proposed a class of counterexamples to this principle involving the ability to know certain propositions. I renew an argument against these counterexamples based on the unknowability of Fitch propositions. In doing so, I provide a new argument for the unknowability of Fitch propositions and show that Spencer’s counterexamples are in tension with a principle (...) weaker than the one linking abilities and possibilities. (shrink)

We present a framework for epistemic logic, modeling the logical aspects of System 1 and System 2 cognitive processes, as per dual process theories of reasoning. The framework combines non-normal worlds semantics with the techniques of Dynamic Epistemic Logic. It models non-logically-omniscient, but moderately rational agents: their System 1 makes fast sense of incoming information by integrating it on the basis of their background knowledge and beliefs. Their System 2 allows them to slowly, step-wise unpack some of the logical consequences (...) of such knowledge and beliefs, by paying a cognitive cost. The framework is applied to three instances of limited rationality, widely discussed in cognitive psychology: Stereotypical Thinking, the Framing Effect, and the Anchoring Effect. (shrink)

Marton ( 2019 ) argues that that it follows from the standard antirealist theory of truth, which states that truth and possible knowledge are equivalent, that knowing possibilities is equivalent to the possibility of knowing, whereas these notions should be distinct. Moreover, he argues that the usual strategies of dealing with the Church–Fitch paradox of knowability are either not able to deal with his modal-epistemic collapse result or they only do so at a high price. Against this, I argue that (...) Marton’s paper does not present any seriously novel challenge to anti-realism not already found in the Church–Fitch result. Furthermore, Edgington ( 1985 ) reformulated antirealist theory of truth can deal with his modal-epistemic collapse argument at no cost. (shrink)

The principle of epistemic closure is the claim that what is known to follow from knowledge is known to be true. This intuitively plausible idea is endorsed by a vast majority of knowledge theorists. There are significant problems, however, that have to be addressed if epistemic closure – closed knowledge – is endorsed. The present essay locates the problem for closed knowledge in the separation it imposes between knowledge and evidence. Although it might appear that all that stands between knowing (...) the truth of the premises of a valid inference and knowledge of its conclusion is inferring it from the premises, the evidence for each of the premises may jointly count against the conclusion. The intuitive view regarding inferred knowledge says one thing, the evidence says another. One epistemological framework that seems to have the resources to resolve this tension endorses the view that knowledge always requires conclusive evidence. A second framework resolves the tension by limiting the scope of the closure principle. Only inferences drawn directly from propositions contained in the scope of a single knowledge operator are considered closed. The aim of the present essay is to revive the unpopular third option, the idea that knowledge is open. The essay proceeds by arguing that in different ways the two former frameworks only succeed in relocating the problem, not in resolving it. The first framework, the infallibilist view, relocates the problem to a sharp separation between knowledge of the occurrences of events from knowledge of their chance of occurring, a separation leading to several significant additional problems. The fallibilist view, the second framework, in endorsing closure neglects to take into full account the ways in which evidence fails to be transitive. For instance, evidence can count in favor of a conjunction while counting against each of its conjuncts. This fact, which is argued for in the essay on probabilistic as well as non-probabilistic grounds, is used as the foundation of an argument against closed knowledge that can be used as a way to understand several of the most fundamental challenges of epistemology. Not only can an open knowledge view that is based on open evidence resolve all these problems in a simple and natural way, it can also respond to formidable challenges that significantly hinder other open knowledge views. There are good reasons, then, to view both knowledge and evidence as open. (shrink)

We propose that, for the purpose of studying theoretical properties of the knowledge of an agent with Artificial General Intelligence (that is, the knowledge of an AGI), a pragmatic way to define such an agent’s knowledge (restricted to the language of Epistemic Arithmetic, or EA) is as follows. We declare an AGI to know an EA-statement φ if and only if that AGI would include φ in the resulting enumeration if that AGI were commanded: “Enumerate all the EA-sentences which you (...) know.” This definition is non-circular because an AGI, being capable of practical English communication, is capable of understanding the everyday English word “know” independently of how any philosopher formally defines knowledge; we elaborate further on the non-circularity of this circular-looking definition. This elegantly solves the problem that different AGIs may have different internal knowledge definitions and yet we want to study knowledge of AGIs in general, without having to study different AGIs separately just because they have separate internal knowledge definitions. Finally, we suggest how this definition of AGI knowledge can be used as a bridge which could allow the AGI research community to import certain abstract results about mechanical knowing agents from mathematical logic. (shrink)

This paper aims to provide a mathematically tractable background against which to model both modal cognitivism and modal expressivism. I argue that epistemic modal algebras, endowed with a hyperintensional, topic-sensitive epistemic two-dimensional truthmaker semantics, comprise a materially adequate fragment of the language of thought. I demonstrate, then, how modal expressivism can be regimented by modal coalgebraic automata, to which the above epistemic modal algebras are categorically dual. I examine five methods for modeling the dynamics of conceptual engineering for intensions and (...) hyperintensions. I develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic epistemic two-dimensional hyperintensional semantics. I examine then the virtues unique to the modal expressivist approach here proffered in the setting of the foundations of mathematics, by contrast to competing approaches based upon both the inferentialist approach to concept-individuation and the codification of speech acts via intensional semantics. (shrink)

We consider a basic logic with two primitive uni-modal operators: one for certainty and the other for plausibility. The former is assumed to be a normal operator, while the latter is merely a classical operator. We then define belief, interpreted as “maximally plausible possibility”, in terms of these two notions: the agent believes \ if she cannot rule out \ ), she judges \ to be plausible and she does not judge \ to be plausible. We consider four interaction properties (...) between certainty and plausibility and study how these properties translate into properties of belief. We then prove that all the logics considered are minimal logics for the highlighted theorems. We also consider a number of possible interpretations of plausibility, identify the corresponding logics and show that some notions considered in the literature are special cases of our framework. (shrink)

Recent years have witnessed a proliferation of attempts to apply the mathematical theory of probability to the semantics of natural language probability talk. These sorts of “probabilistic” semantics are often motivated by their ability to explain intuitions about inferences involving “likely” and “probably”—intuitions that Angelika Kratzer’s canonical semantics fails to accommodate through a semantics based solely on an ordering of worlds and a qualitative ranking of propositions. However, recent work by Wesley Holliday and Thomas Icard has been widely thought to (...) undercut this motivation: they present a world-ordering semantics that yields essentially the same logic as probabilistic semantics. In this paper, I argue that the challenge remains: defenders of world-ordering semantics have yet to offer a plausible semantics that captures the logic of comparative likelihood. Holliday & Icard’s semantics yields an adequate logic only if models are restricted to Noetherian pre-orders. But I argue that the Noetherian restriction faces problems in cases involving infinitely large domains of epistemic possibilities. As a result, probabilistic semantics remains the better explanation of the data. (shrink)

Weakly Aggregative Modal Logic (WAML) is a collection of disguised polyadic modal logics with n-ary modalities whose arguments are all the same. WAML has some interesting applications on epistemic logic and logic of games, so we study some basic model theoretical aspects of WAML in this paper. Specifically, we give a van Benthem-Rosen characterization theorem of WAML based on an intuitive notion of bisimulation and show that each basic WAML system Kn lacks Craig Interpolation.

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)

On at least one of its uses, ‘higher-order evidence’ refers to evidence about what opinions are rationalized by your evidence. This chapter surveys the foundational epistemological questions raised by such evidence, the methods that have proven useful for answering them, and the potential consequences and applications of such answers.

This paper investigates and develops generalizations of two-dimensional modal logics to any finite dimension. These logics are natural extensions of multidimensional systems known from the literature on logics for a priori knowledge. We prove a completeness theorem for propositional n-dimensional modal logics and show them to be decidable by means of a systematic tableau construction.

In recent years, some authors have proposed quantitative measures of the coherence of sets of propositions. Such probabilistic measures of coherence (PMCs) are, in general terms, functions that take as their argument a set of propositions (along with some probability distribution) and yield as their value a number that is supposed to represent the degree of coherence of the set. In this paper, I introduce a minimal constraint on PMC theories, the weak stability principle, and show that any correct, coherent, (...) and complete PMC cannot satisfy it. As a matter of fact, the argument offered in this paper can be applied to any coherence theory that uses a priori procedures. I briefly explore some consequences of this fact. (shrink)

Zero and one is circumference and diameter. Literally. And, figuratively.

The relevance of any logical analysis lies in its ability to solve paradoxes and trace conceptual troubles back; with this respect, the task of epistemic logic is to handle paradoxes in connection with the concept of knowledge. Epistemic logic is currently introduced as the logical analysis of crucial concepts within epistemology, namely: knowledge, belief, truth, and justification. An alternative approach will be advanced here in order to enlighten such a discourse, as centred upon the word assertion and displayed in terms (...) of utterance. Insofar as epistemic modalities express some attitudes, the intentionality of discourse will be emphasized within an illocutionary modal logic. Two large views will range over the whole study: declarative and epistemic sentences have one and the same logic (assertion logic); the plurality of languages games doesn’t entail any logical pluralism. -/- La valeur d'une analyse logique réside dans sa capacité à résoudre des paradoxes et à comprendre l'origine de nos problèmes conceptuels ; à ce titre, le rôle d'une logique épistémique est de traiter des paradoxes liés au concept de connaissance. On présente généralement la logique épistémique comme une analyse logique de concepts centraux en épistémologie : connaissance, croyance, vérité, justification. Une autre approche sera proposée ici en vue de clarifier ce genre de discours, centrée sur la notion d'assertion et décrite en termes d'énonciation. Parce que les modalités épistémiques expriment des attitudes, c'est l'intentionnalité du discours qui sera mise en valeur dans le cadre d'une logique modale illocutoire. Deux thèses transversales parcourront l'ensemble du travail : les énoncés déclaratifs et épistémiques partagent la même logique (logique assertorique) ; la pluralité des jeux de langages n'implique pas un pluralisme logique. (shrink)

The present paper wants to promote epistemic pluralism as an alternative view of non-classical logics. For this purpose, a bilateralist logic of acceptance and rejection is developed in order to make an important di erence between several concepts of epistemology, including information and justi cation. Moreover, the notion of disagreement corresponds to a set of epistemic oppositions between agents. The result is a non-standard theory of opposition for many-valued logics, rendering total and partial disagreement in terms of epistemic negation and (...) semi-negations. (shrink)

How do people reason about their opponent in turn-taking games? Often, people do not make the decisions that game theory would prescribe. We present a logic that can play a key role in understanding how people make their decisions, by delineating all plausible reasoning strategies in a systematic manner. This in turn makes it possible to construct a corresponding set of computational models in a cognitive architecture. These models can be run and fitted to the participants’ data in terms of (...) decisions, response times, and answers to questions. We validate these claims on the basis of an earlier game-theoretic experiment about the turn-taking game “Marble Drop with Surprising Opponent”, in which the opponent often starts with a seemingly irrational move. We explore two ways of segregating the participants into reasonable “player types”. The first way is based on latent class analysis, which divides the players into three classes according to their first decisions in the game: Random players, Learners, and Expected players, who make decisions consistent with forward induction. The second way is based on participants’ answers to a question about their opponent, classified according to levels of theory of mind: zero-order, first-order and second-order. It turns out that increasing levels of decisions and theory of mind both correspond to increasing success as measured by monetary awards and increasing decision times. Next, we use the logical language to express different kinds of strategies that people apply when reasoning about their opponent and making decisions in turn-taking games, as well as the ‘reasoning types’ reflected in their behavior. Then, we translate the logical formulas into computational cognitive models in the PRIMs architecture. Finally, we run two of the resulting models, corresponding to the strategy of only being interested in one’s own payoff and to the myopic strategy, in which one can only look ahead to a limited number of nodes. It turns out that the participant data fit to the own-payoff strategy, not the myopic one. The article closes the circle from experiments via logic and cognitive modelling back to predictions about new experiments. (shrink)

You have higher-order uncertainty iff you are uncertain of what opinions you should have. I defend three claims about it. First, the higher-order evidence debate can be helpfully reframed in terms of higher-order uncertainty. The central question becomes how your first- and higher-order opinions should relate—a precise question that can be embedded within a general, tractable framework. Second, this question is nontrivial. Rational higher-order uncertainty is pervasive, and lies at the foundations of the epistemology of disagreement. Third, the answer is (...) not obvious. The Enkratic Intuition---that your first-order opinions must “line up” with your higher-order opinions---is incorrect; epistemic akrasia can be rational. If all this is right, then it leaves us without answers---but with a clear picture of the question, and a fruitful strategy for pursuing it. (shrink)

Kant's theory of transcendental ideas can be conceived as a sort of model theory for an empirical first-order object theory. The main features of Kant's theory of transcendental ideas (especially its antinomies and their solutions) can be recognized, in a modified way, in a religious discourse as exemplified in the dialogue of Jesus and the Samaritan woman (John 4). In this way, what is by Kant meant merely as regulative ideas obtains a sort of objective reality and becomes a religiously (...) founded metaphysics. A metaphysical theory of religious dialogue is formalized on the basis of an extended justification logic of evidence and wish agents. (shrink)

Justification logics are constructive analogues of modal logics. They are often used as epistemic logics, particularly as models of evidentialist justification. However, in this role, justification (and modal) logics are defective insofar as they represent justification with a necessity-like operator, whereas actual evidentialist justification is usually probabilistic. This paper first examines and rejects extant candidates for solving this problem: Milnikel’s Logic of Uncertain Justifications, Ghari’s Hájek–Pavelka-Style Justification Logics and a version of probabilistic justification logic developed by Kokkinis et al. It (...) then proposes a new solution to the problem in the form of a justification logic that incorporates the essential features of both a fuzzy logic and a probabilistic logic. (shrink)

This paper is concerned with representations of belief by means of nonadditive probabilities of the Dempster-Shafer (DS) type. After surveying some foundational issues and results in the D.S. theory, including Suppes's related contributions, the paper proceeds to analyze the connection of the D.S. theory with some of the work currently pursued in epistemic logic. A preliminary investigation of the modal logic of belief functions à la Shafer is made. There it is shown that the Alchourrron-Gärdenfors-Makinson (A.G.M.) logic of belief change (...) is closely related to the D.S. theory. The final section compares the critique of Bayesianism which underlies the present paper with some important objections raised by Suppes against this doctrine. -/- . (shrink)

After a number of decades of research into the dynamics of rational belief, the belief revision theory community remains split on the appropriate handling of sequences of changes in view, the issue of so-called iterated revision. It has long been suggested that the matter is at least partly settled by facts pertaining to the results of various single revisions of one’s initial state of belief. Recent work has pushed this thesis further, offering various strong principles that ultimately result in a (...) wholesale reduction of iterated to one-shot revision. The present paper offers grounds to hold that these principles should be significantly weakened and that the reductionist thesis should ultimately be rejected. Furthermore, the considerations provided suggest a close connection between the logic of iterated belief change and the logic of evidential relevance. (shrink)

This paper targets a series of potential issues for the discussion of, and modal resolution to, the alethic paradoxes advanced by Scharp (2013). I proffer four novel extensions of the theory, and detail five issues that the theory faces.

This essay provides a novel account of iterated epistemic states. The essay argues that states of epistemic determinacy might be secured by countenancing iterated epistemic states on the model of fixed points in the modal $\mu$-calculus. Despite the epistemic indeterminacy witnessed by the invalidation of modal axiom 4 in the sorites paradox -- i.e. the KK principle: $\square$$\phi$ $\rightarrow$ $\square$$\square$$\phi$ -- a hyperintensional epistemic $\mu$-automaton permits fixed points to entrain a principled means by which to iterate epistemic states and account (...) thereby for necessary conditions on self-knowledge. The hyperintensional epistemic $\mu$-calculus is applied to the iteration of the epistemic states of a single agent instead of the common knowledge of a group of agents, and is thus a novel contribution to the literature. (shrink)

This book concerns the foundations of epistemic modality and hyperintensionality and their applications to the philosophy of mathematics. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality and hyperintensionality relate to the computational theory of mind; metaphysical modality and hyperintensionality; the types of mathematical modality and hyperintensionality; to the epistemic status of large cardinal axioms, undecidable propositions, (...) and abstraction principles in the philosophy of mathematics; to the modal and hyperintensional profiles of the logic of rational intuition; and to the types of intention, when the latter is interpreted as a hyperintensional mental state. Chapter 2 argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal cognitivism and modal expressivism. I also develop a novel topic-sensitive truthmaker semantics for dynamic epistemic logic, and develop a novel dynamic epistemic two-dimensional hyperintensional semantics. Chapter 3 provides an abstraction principle for epistemic (hyper-)intensions. Chapter 4 advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter 5 applies the fixed points of the modal μ-calculus in order to account for the iteration of epistemic states in a single agent, by contrast to availing of modal axiom 4 (i.e. the KK principle). The fixed point operators in the modal μ-calculus are rendered hyperintensional, which yields the first hyperintensional construal of the modal μ-calculus in the literature and the first application of the calculus to the iteration of epistemic states in a single agent instead of the common knowledge of a group of agents. Chapter 6 advances a solution to the Julius Caesar problem based on Fine's `criterial' identity conditions which incorporate conditions on essentiality and grounding. Chapter 7 provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapters 2 and 4 are availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. -/- Chapters 8-12 provide cases demonstrating how the two-dimensional hyperintensions of hyperintensional, i.e. topic-sensitive epistemic two-dimensional truthmaker, semantics, solve the access problem in the epistemology of mathematics. Chapter 8 examines the interaction between my hyperintensional semantics and the axioms of epistemic set theory, large cardinal axioms, the Epistemic Church-Turing Thesis, the modal axioms governing the modal profile of Ω-logic, Orey sentences such as the Generalized Continuum Hypothesis, and absolute decidability. These results yield inter alia the first hyperintensional Epistemic Church-Turing Thesis and hyperintensional epistemic set theories in the literature. Chapter 9 examines the modal and hyperintensional commitments of abstractionism, in particular necessitism, and epistemic hyperintensionality, epistemic utility theory, and the epistemology of abstraction. I countenance a hyperintensional semantics for novel epistemic abstractionist modalities. I suggest, too, that observational type theory can be applied to first-order abstraction principles in order to make first-order abstraction principles recursively enumerable, i.e. Turing machine computable, and that the truth of the first-order abstraction principle for hyperintensions is grounded in its being possibly recursively enumerable and the machine being physically implementable. Chapter 10 examines the philosophical significance of hyperintensional Ω-logic in set theory and discusses the hyperintensionality of metamathematics. Chapter 11 provides a modal logic for rational intuition and provides a hyperintensional semantics. Chapter 12 avails of modal coalgebras to interpret the defining properties of indefinite extensibility, and avails of hyperintensional epistemic two-dimensional semantics in order to account for the interaction between the interpretational and objective modalities and truthmakers thereof. This yields the first hyperintensional category theory in the literature. I invent a new mathematical trick in which first order structures are treated as categories, and Vopenka's principle can be satisfied because of the elementary embeddings between the categories and generate Vopenka cardinals while bypassing the category of Set in category theory. Chapter 13 examines modal responses to the alethic paradoxes. Chapter 14 examines, finally, the modal and hyperintensional semantics for the different types of intention and the relation of the latter to evidential decision theory. (shrink)

Review of Joseph Y. Halpern (ed.), Theoretical Aspects of Reasoning About Knowledge: Proceedings of the 1986 Conference (Los Altos, CA: Morgan Kaufmann, 1986),.

This article takes off from Johan van Benthem’s ruminations on the interface between logic and cognitive science in his position paper “Logic and reasoning: Do the facts matter?”. When trying to answer Van Benthem’s question whether logic can be fruitfully combined with psychological experiments, this article focuses on a specific domain of reasoning, namely higher-order social cognition, including attributions such as “Bob knows that Alice knows that he wrote a novel under pseudonym”. For intelligent interaction, it is important that the (...) participants recursively model the mental states of other agents. Otherwise, an international negotiation may fail, even when it has potential for a win-win solution, and in a time-critical rescue mission, a software agent may depend on a teammate’s action that never materializes. First a survey is presented of past and current research on higher-order social cognition, from the various viewpoints of logic, artificial intelligence, and psychology. Do people actually reason about each other’s knowledge in the way proscribed by epistemic logic? And if not, how can logic and cognitive science productively work together to construct more realistic models of human reasoning about other minds? The paper ends with a delineation of possible avenues for future research, aiming to provide a better understanding of higher-order social reasoning. The methodology is based on a combination of experimental research, logic, computational cognitive models, and agent-based evolutionary models. (shrink)

An introduction to the special issue on epistemic logic and the foundations of game theory edited by Michael Bacharach and Philippe Mongin. Contributors are Michael Bacharach, Robert Stalnaker, Salvatore Modica and Aldo Rustichini, Luc Lismont and Philippe Mongin, and Hyun-Song Shin and Timothy Williamson.

This French paper is a prelimary report on the authors' work on the logics of common knowledge and common belief. See L. Lismont and P. Mongin, "On the logic of common belief and common knowledge", Theory and Decision 37 (1): 75-106. 1994 for a more complete report.

Using a knowledge-based approach, we derive a protocol, MACOM1, for the sequence transmission problem from one agent to a group of agents. The protocol is correct for communication media where deletion and reordering errors may occur. Furthermore, it is shown that after k rounds the agents in the group attain depth k general knowledge about the members of the group and the values of the messages. Then, we adjust this algorithm for multi-agent communication for the process of teamwork. MACOM1 solves (...) the sequence transmission problem from one agent to a group of agents, but does not fully comply with the type of dialogue communication needed for teamwork. The number of messages being communicated per communication between the initiator and the other agents from the group can differ. Furthermore, the teamwork process can require the communication algorithm to handle changes of initiator. We show the adjustments that have to be made to MACOM1 to handle these properties of teamwork. For the new multi-agent communication algorithm, MACOM2, it is shown that the gaining of knowledge required for a successful teamwork process is still guaranteed. (shrink)

The paper surveys the currently available axiomatizations of common belief (CB) and common knowledge (CK) by means of modal propositional logics. (Throughout, knowledge- whether individual or common- is defined as true belief.) Section 1 introduces the formal method of axiomatization followed by epistemic logicians, especially the syntax-semantics distinction, and the notion of a soundness and completeness theorem. Section 2 explains the syntactical concepts, while briefly discussing their motivations. Two standard semantic constructions, Kripke structures and neighbourhood structures, are introduced in Sections (...) 3 and 4, respectively. It is recalled that Aumann's partitional model of CK is a particular case of a definition in terms of Kripke structures. The paper also restates the well-known fact that Kripke structures can be regarded as particular cases of neighbourhood structures. Section 3 reviews the soundness and completeness theorems proved w.r.t. the former structures by Fagin, Halpern, Moses and Vardi, as well as related results by Lismont. Section 4 reviews the corresponding theorems derived w.r.t. the latter structures by Lismont and Mongin. A general conclusion of the paper is that the axiomatization of CB does not require as strong systems of individual belief as was originally thought- only monotonicity has thusfar proved indispensable. Section 5 explains another consequence of general relevance: despite the "infinitary" nature of CB, the axiom systems of this paper admit of effective decision procedures, i.e., they are decidable in the logician's sense. (shrink)

This article takes off from Johan van Benthem’s ruminations on the interface between logic and cognitive science in his position paper “Logic and reasoning: Do the facts matter?”. When trying to answer Van Benthem’s question whether logic can be fruitfully combined with psychological experiments, this article focuses on a specific domain of reasoning, namely higher-order social cognition, including attributions such as “Bob knows that Alice knows that he wrote a novel under pseudonym”. For intelligent interaction, it is important that the (...) participants recursively model the mental states of other agents. Otherwise, an international negotiation may fail, even when it has potential for a win-win solution, and in a time-critical rescue mission, a software agent may depend on a teammate’s action that never materializes. First a survey is presented of past and current research on higher-order social cognition, from the various viewpoints of logic, artificial intelligence, and psychology. Do people actually reason about each other’s knowledge in the way proscribed by epistemic logic? And if not, how can logic and cognitive science productively work together to construct more realistic models of human reasoning about other minds? The paper ends with a delineation of possible avenues for future research, aiming to provide a better understanding of higher-order social reasoning. The methodology is based on a combination of experimental research, logic, computational cognitive models, and agent-based evolutionary models. Keywords Epistemic logic - Cognitive science - Intelligent interaction - Cognitive modeling. (shrink)