In this paper we design a new logical system to explicitly model the different deductive reasoning steps of a boundedly rational agent. We present an adequate system in line with experimental findings about an agent’s reasoning limitations and the cognitive effort that is involved. Inspired by Dynamic Epistemic Logic, we work with dynamic operators denoting explicit applications of inference rules in our logical language. Our models are supplemented by (a) impossible worlds (not closed under logical consequence), suitably structured according to (...) the effect of inference rules, and (b) quantitative components capturing the agent’s cognitive capacity and the cognitive costs of rules with respect to certain resources (e.g. memory, time). These ingredients allow us to avoid problematic logical closure principles, while at the same time deductive reasoning is reflected in our dynamic truth clauses. We further show that our models can be reduced to awareness-like plausibility structures that validate the same formulas and we give a sound and complete axiomatization with respect to them. This approach to the agent’s internal deductive reasoning is finally combined with actions of external information. (shrink)

Among the non-monotonic reasoning processes, abduction is one of the most important. Usually described as the process of looking for explanations, it has been recognized as one of the most commonly used in our daily activities. Still, the traditional definitions of an abductive problem and an abductive solution mention only theories and formulas, leaving agency out of the picture. Our work proposes a study of abductive reasoning from an epistemic and dynamic perspective. In the first part we explore syntactic definitions (...) of both an abductive problem in terms of an agent’s information and an abductive solution in terms of the actions that modify the agent’s information. We look at diverse kinds of agents, including not only omniscient ones but also those whose information is not closed under logical consequence and those whose reasoning abilities are not complete. In the second part, we look at an existing logical framework whose semantic model allows us to interpret the previously stated formulas, and we define two actions that represent forms of abductive reasoning. (shrink)

We motivate a picture of social epistemology that sees forgetting as subject to epistemic evaluation. Using computer simulations of a simple agent-based model, we show that how agents forget can have as large an impact on group epistemic outcomes as how they share information. But, how we forget, unlike how we form beliefs, isn’t typically taken to be the sort of thing that can be epistemically rational or justified. We consider what we take to be the most promising argument for (...) this claim and find it lacking. We conclude that understanding how agents forget should be as central to social epistemology as understanding how agents form beliefs and share information with others. (shrink)

Among the many possible approaches to dealing with logical omniscience, I consider here awareness and impossible worlds structures. The former approach, pioneered by Fagin and Halpern, distinguishes between implicit and explicit knowledge, and avoids logical omniscience with respect to explicit knowledge. The latter, developed by Rantala and by Hintikka, allows for the existence of logically impossible worlds to which the agents are taken to have access; since such worlds need not behave consistently, the agents’ knowledge is fallible relative to logical (...) omniscience. The two approaches are known to be equally expressive in propositional systems interpreted over Kripke semantics. In this paper I show that the two approaches are equally expressive in propositional systems interpreted over Montague-Scott (neighborhood) semantics. Furthermore, I provide predicate systems of both awareness and impossible worlds structures interpreted on neighborhood semantics and prove the two systems to be equally expressive. (shrink)

Real-world agents do not know all consequences of what they know. But we are reluctant to say that a rational agent can fail to know some trivial consequence of what she knows. Since every consequence of what she knows can be reached via chains of trivial cot be dismissed easily, as some have attempted to do. Rather, a solution must give adequate weight to the normative requirements on rational agents’ epistemic states, without treating those agents as mathematically ideal reasoners. I’ll (...) argue that agents can fail to know trivial consequences of what they know, but never determinately. Such cases are epistemic oversights on behalf of the agent in question, and the facts about epistemic oversights are always indeterminate facts. As a result, we are never in a position to assert that such-and-such constitutes an epistemic oversight for agent i (for we may rationally assert only determinate truths). I then develop formal epistemic models according to which epistemic accessibility relations are vague. Given these models, we can show that epistemic oversights always concern indeterminate cases of knowledge. (shrink)

In the last decade the concept of context has been extensivelyexploited in many research areas, e.g., distributed artificialintelligence, multi agent systems, distributed databases, informationintegration, cognitive science, and epistemology. Three alternative approaches to the formalization of the notion ofcontext have been proposed: Giunchiglia and Serafini's Multi LanguageSystems (ML systems), McCarthy's modal logics of contexts, andGabbay's Labelled Deductive Systems.Previous papers have argued in favor of ML systems with respect to theother approaches. Our aim in this paper is to support these arguments froma (...) theoretical perspective. We provide a very general definition of ML systems, which covers allthe ML systems used in the literature, and we develop a proof theoryfor an important subclass of them: the MR systems. We prove variousimportant results; among other things, we prove a normal form theorem,the sub-formula property, and the decidability of an importantinstance of the class of the MR systems. The paper concludes with a detailed comparison among the alternativeapproaches. (shrink)

We introduce a general representation of unary hyperintensional modalities and study various hyperintensional modal logics based on the representation. It is shown that the major approaches to hyperintensionality known from the literature, that is state-based, syntactic and structuralist approaches, all correspond to special cases of the general framework. Completeness results pertaining to our hyperintensional modal logics are established.

In this paper, I will develop a set of boulesic-doxastic tableau systems and prove that they are sound and complete. Boulesic-doxastic logic consists of two main parts: a boulesic part and a doxastic part. By ‘boulesic logic’ I mean ‘the logic of the will’, and by ‘doxastic logic’ I mean ‘the logic of belief’. The first part deals with ‘boulesic’ concepts, expressions, sentences, arguments and theorems. I will concentrate on two types of boulesic expression: ‘individual x wants it to be (...) the case that’ and ‘individual x accepts that it is the case that’. The second part deals with ‘doxastic’ concepts, expressions, sentences, arguments and theorems. I will concentrate on two types of doxastic expression: ‘individual x believes that’ and ‘it is imaginable to individual x that’. Boulesic-doxastic logic investigates how these concepts are related to each other. Boulesic logic is a new kind of logic. Doxastic logic has been around for a while, but the approach to this branch of logic in this paper is new. Each system is combined with modal logic with two kinds of modal operators for historical and absolute necessity and predicate logic with necessary identity and ‘possibilist’ quantifiers. I use a kind of possible world semantics to describe the systems semantically. I also sketch out how our basic language can be extended with propositional quantifiers. All the systems developed in this paper are new. (shrink)

In this paper, I develop a new set of doxastic logical systems and I show how they can be used to solve several well-known problems in doxastic logic, for example the so-called problem of logical omniscience. According to this puzzle, the notions of knowledge and belief that are used in ordinary epistemic and doxastic symbolic systems are too idealised. Hence, those systems cannot be used to model ordinary human or human-like agents' beliefs. At best, they can describe idealised individuals. The (...) systems in this paper can be used to symbolise not only the doxastic states of perfectly rational individuals, but also the beliefs of finite humans. Proof-theoretically, I will use a tableau technique. Every system is combined with predicate logic with necessary identity and ‘possibilist’ quantifiers and modal logic with two kinds of modal operators for relative and absolute necessity. The semantics is a possible world semantics. Finally, I prove that every tableau system in the paper is sound and complete with respect to its semantics. (shrink)

Inspired by the recent work on approximations of classical logic, we present a method that approximates several modal logics in a modular way. Our starting point is the limitation of the n-degree of introspection that is allowed, thus generating modaln-logics. The semantics for n-logics is presented, in which formulas are evaluated with respect to paths, and not possible worlds. A tableau-based proof system is presented, n-SST, and soundness and completeness is shown for the approximation of modal logics image and image.

This paper introduces a multi-agent dynamic epistemic logic for abstract argumentation. Its main motivation is to build a general framework for modelling the dynamics of a debate, which entails reasoning about goals, beliefs, as well as policies of communication and information update by the participants. After locating our proposal and introducing the relevant tools from abstract argumentation, we proceed to build a three-tiered logical approach. At the first level, we use the language of propositional logic to encode states of a (...) multi-agent debate. This language allows to specify which arguments any agent is aware of, as well as their subjective justification status. We then extend our language and semantics to that of epistemic logic, in order to model individuals’ beliefs about the state of the debate, which includes uncertainty about the information available to others. As a third step, we introduce a framework of dynamic epistemic logic and its semantics, which is essentially based on so-called event models with factual change. We provide completeness results for a number of systems and show how existing formalisms for argumentation dynamics and unquantified uncertainty can be reduced to their semantics. The resulting framework allows reasoning about subtle epistemic and argumentative updates—such as the effects of different levels of trust in a source—and more in general about the epistemic dimensions of strategic communication. (shrink)

This work proposes an understanding of deductive, default and abductive reasoning as different instances of the same phenomenon: epistemic dynamics. It discusses the main intuitions behind each one of these reasoning processes, and suggest how they can be understood as different epistemic actions that modify an agent’s knowledge and/or beliefs in a different way, making formal the discussion with the use of the dynamic epistemic logic framework. The ideas in this paper put the studied processes under the same umbrella, thus (...) highlighting their relationship and allowing a better understanding of how they interact together. (shrink)

This paper puts forth a class of algebraic structures, relativized Boolean algebras (RBAs), that provide semantics for propositional logic in which truth/validity is only defined relative to a local domain. In particular, the join of an event and its complement need not be the top element. Nonetheless, behavior is locally governed by the laws of propositional logic. By further endowing these structures with operators—akin to the theory of modal Algebras—RBAs serve as models of modal logics in which truth is relative. (...) In particular, modal RBAs provide semantics for various well-known awareness logics and an alternative view of possibility semantics. (shrink)

In the real world, there can be constraints on rational decision-making: there can be limitations on what I can know and on what you can know. There can also be constraints on my ability to deliberate or on your ability to deliberate. It is useful to know what the norms of rational deliberation should be in ideal contexts, for fully informed agents, in an ideal world. But it is also useful to know what the norms of rational deliberation should be (...) in the actual world, in non-ideal contexts, for imperfectly informed agents, especially for big, life-changing decisions. That is, we want to know how to deliberate as best we can, given the real-world limitations on what we can know, and given real-world limitations on how we are able to deliberate. In this paper, our concern is with the norms of rational deliberation in certain, important, non-ideal contexts, where the reasoning occurs from the agent’s first person, subjective point of view. The norms governing the process of deliberation for real people in the sorts of non-ideal contexts we’ll consider need to reflect the way that real agents, with an incomplete grasp on the facts and an imperfect ability to deliberate, can be expected to proceed. Our central contention is that framing and exploring the deliberative process from the first person perspective allows us to uncover and explore important, real-world constraints on boundedly rational agents deliberating from the subjective perspective. (shrink)

One fundamental assumption often made in the literature on unawareness is that risk preferences are invariant to changes of awareness. We study how exposure to unawareness affects choices under risk. Participants in our experiment choose repeatedly between varying sure outcomes and a lottery in three phases. All treatments are exactly identical in phase 1 and phase 3, but differ in phase 2. There are five different treatments pertaining to the lottery faced in phase 2: The control treatment, the treatment with (...) awareness of unawareness of lottery outcomes but known number of outcomes, the treatment with awareness of unawareness of outcomes but with unknown number of outcomes, the treatment with unawareness of unawareness of some outcomes, and the treatment with an ambiguous lottery. We study both whether behavior differs in phase 3 across treatments and whether differences of subjects’ behavior between phases 1 and phase 3 differ across treatments. We observe no significant treatment effects. (shrink)

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)

This is the introduction of the special issue,.

Vlastos’ famous characterization of the Socratic elenchus focuses on two main aspects of this method: its epistemic roots and its dialogical nature. Our aim is to lay the groundwork to formally capture this characterization. To do so, first, we outline an epistemic framework in which the elenchus can be inscribed. More precisely, we focus our analysis on the passage from unconscious ignorance to conscious (or Socratic) ignorance and provide new insights about the epistemic outcome of an elenctic argument. Secondly, from (...) a logical perspective, we consider the elenchus as a dynamic exchange allowing Socrates’ respondents to revise their beliefs, on pain of inconsistency. By stressing this point, we represent this method as a process of belief revision in dynamic epistemic logic and provide a new logical solution to what Vlastos called the problem of the elenchus. (shrink)

In the most popular logics combining knowledge and awareness, it is not possible to express statements about knowledge of unawareness such as “Ann knows that Bill is aware of something Ann is not aware of”—without using a stronger statement such as “Ann knows that Bill is aware of \(p\) and Ann is not aware of \(p\) ”, for some particular \(p\) . In Halpern and Rêgo (Proceedings of KR 2006; Games Econ Behav 67(2):503–525, 2009b) Halpern and Rêgo introduced a logic (...) in which such statements about knowledge of unawareness can be expressed. The logic extends the traditional framework with quantification over formulae, and is thus very expressive. As a consequence, it is not decidable. In this paper we introduce a decidable logic which can be used to reason about certain types of unawareness. Our logic extends the traditional framework with an operator expressing full awareness, i.e., the fact that an agent is aware of everything, and another operator expressing relative awareness, the fact that one agent is aware of everything another agent is aware of. The logic is less expressive than Halpern’s and Rêgo’s logic. It is, however, expressive enough to express all of the motivating examples in Halpern and Rêgo (Proceedings of KR 2006; Games Econ Behav 67(2):503–525, 2009b). In addition to proving that the logic is decidable and that its satisfiability problem is PSPACE-complete, we present an axiomatisation which we show is sound and complete. (shrink)

In recent work MacPherson argues that the standard method of modeling belief logically, as a necessity operator in a modal logic, is doomed to fail. The problem with normal modal logics as logics of belief is that they treat believers as "ideal" in unrealistic ways (i.e., as omnidoxastic); however, similar problems re-emerge for candidate non-normal logics. The authors argue that logics used to model belief in artificial intelligence (AI) are also flawed in this way. But for AI systems, omnidoxasticity is (...) impossible because of their finite nature, and this fact can be exploited to produce operational models of fallible belief. The relevance of this point to various philosophical views about belief is discussed. (shrink)

. The current literature in the Artificial Intelligence and Law field reveals uncertainty concerning the potential role of deontic logic in legal knowledge representation. For instance, the Logic Programming Group at Imperial College has shown that a good deal can be achieved in this area in the absence of explicit representation of the deontic notions. This paper argues that some rather ordinary parts of the law contain structures which, if they are to be represented in logic, will call for use (...) of a reasonably sophisticated deontic logic. (shrink)

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)

The phrase ‘autoepistemic logic’ was introduced in Moore [1985] to refer to a study inspired in large part by criticisms in Stalnaker [1980] of a particular nonmonotonic logic proposed by McDermott and Doyle.1 Very informative discussions for those who have not encountered this area are provided by Moore [1988] and the wide-ranging survey article Konolige [1994], and the scant remarks in the present introductory section do not pretend to serve in place of those treatments as summaries of the field. A (...) good deal of the material omitted here pertains to the specifically nonmonotonic nature of autoepistemic logic as standardly developed, but as we shall urge, there is from one point of view nothing distinctively nonmonotonic about the basic motivating ideas of the subject. (shrink)

This paper surveys the interface between the two major logical trends that describe agents’ intelligent interaction over time: dynamic epistemic logic (DEL) and epistemic temporal logic (ETL). The initial attempt to “merge” DEL and ETL was made in van Benthem et al. (Merging frameworks for interaction: DEL and ETL, 2007) and followed up by van Benthem et al. (J Phil Logic 38(5):491–526, 2009) and Hoshi (Epistemic dynamics and protocol information. Ph.D. thesis, Stanford University Stanford, 2009a). The merged framework provides a (...) systematic comparison between these two logical systems and studies new logics of intelligent interaction. This paper presents the main results and the recent developments at the interface between DEL and ETL. (shrink)

It is well-known that classical models of belief are not realistic representations of human doxastic capacity; equally, models of actions involving beliefs, such as decisions based on beliefs, or changes of beliefs, suffer from a similar inaccuracies. In this paper, a general framework is presented which permits a more realistic modelling both of instantaneous states of belief, and of the operations involving them. This framework is motivated by some of the inadequacies of existing models, which it overcomes, whilst retaining technical (...) rigour in so far as it relies on known, natural logical and mathematical notions. The companion paper (Towards a “sophisticated” model of belief dynamics. Part II) contains an application of this framework to the particular case of belief revision. (shrink)

There has been a recent surge of interest among economists in developing models of doxastic states that can account for some aspects of human cognitive limitations that are ignored by standard formal models, such as awareness. Epistemologists purport to have a principled reason for ignoring the question of awareness: under the equilibrium conception of doxastic states they favour, a doxastic state comprises the doxastic commitments an agent would recognise were he fully aware, so the question of awareness plays no role. (...) The objective of this paper is to scrutinize this argument. A thesis underlying the argument, which we call the independence of doxastic commitments with respect to awareness, is identified, and examples are given where it appears to be violated. By considering these examples, one can get an idea of the price of accepting this thesis. On the one hand, one can escape the conclusion that the thesis is violated, but only at the expense of another principle espoused by all major formal models of belief, which we call constant doxastic rest; and abandoning this principle necessitates extensive revision of current models of belief. On the other hand, there are epistemologically valid reasons for thinking that the thesis fails to hold in the examples, which have to be rebutted if the thesis, and the equilibrium justification for ignoring the issue of awareness, are to be retained. (shrink)

Of late, evidentiality has received great attention in formal semantics. In this paper I develop ‘evidentiality-informed’ truth conditions for modal operators such as must and may . With language data drawn from Luoping Nase (a Tibeto-Burman language spoken in the P.R. of China and belonging to the Yi Nationality), I illustrate that epistemic modals clash with clauses articulating first-hand information. I then demonstrate that existing models such as Kratzer’s graded possible-worlds semantics fail to provide accurate truth conditions for modals tagging (...) clauses with first-hand information. As a remedy I propose a fuzzy version of possible-worlds semantics with various grades of belief and knowledge. In addition to preserving the expressive power of graded possible-worlds semantics, the fuzzy model will be shown to supply appropriate truth conditions for epistemic modals appended to evidential clauses (i.e. clauses expressing first-hand information). (shrink)

We provide a syntactic model of unawareness. By introducing multiple knowledge modalities, one for each sub-language, we specifically model agents whose only mistake in reasoning (other than their unawareness) is to underestimate the knowledge of more aware agents. We show that the model is a complete and sound axiomatization of the set-theoretic model of Galanis (University of Southampton Discussion paper 709, 2007) and compare it with other unawareness models in the literature.

Deals with the problem of enthymemes in expert systems designed to model legal reasoning; suggests that interactivity is crucial.

One of the open problems in the philosophy of information is whether there is an information logic (IL), different from epistemic (EL) and doxastic logic (DL), which formalises the relation “a is informed that p” (Iap) satisfactorily. In this paper, the problem is solved by arguing that the axiom schemata of the normal modal logic (NML) KTB (also known as B or Br or Brouwer’s system) are well suited to formalise the relation of “being informed”. After having shown that IL (...) can be constructed as an informational reading of KTB, four consequences of a KTB-based IL are explored: information overload; the veridicality thesis (Iap → p); the relation between IL and EL; and the Kp → Bp principle or entailment property, according to which knowledge implies belief. Although these issues are discussed later in the article, they are the motivations behind the development of IL. (shrink)

Logical frameworks that are sensitive to features of sentences’ subject-matter—like Berto’s topic-sensitive intentional modals (TSIMs)—demand a maximally faithful model of the topics of sentences. This is an especially difficult task in the case in which topics are assigned to intensional formulae. In two previous papers, a framework was developed whose model of intensional subject-matter could accommodate a wider range of intuitions about particular intensional conditionals. Although resolving a number of counterintuitive features, the work made an implicit assumption that the subject-matter (...) of an intensional conditional is a function of the subject-matters of its subformulae. This assumption—which I will call a principle of topic sufficiency—runs counter to some natural intuitions concerning topic. In this paper, we will investigate topic sufficiency and offer a semantic account that is state-sensitive, providing an implementation through the introduction of topic-sensitive logics related to William Parry’s prototypical $\mathsf {PAI}$. (shrink)

The paper proposes a logical framework representing the notion of explicit knowledge as the combination of awareness of and awareness that. The setting, semantically combining neighbourhood models with ideas from awareness logic, separates the mere fact of entertaining some information (being aware of $\varphi$) from the acknowledgement that the information is indeed the case (being aware that $\varphi$ holds). The text discusses not only the main properties these concepts obtain under the given representation, but also several of the epistemic actions (...) that can be defined, and the way they affect the agent’s awareness (and thus her knowledge). (shrink)

with this paper, we intend to clarify some of the central notions that are commonly used in contemporary developments of Epistemic Logic, which lack a proper theoretical foundation. We want to follow the steps of some prominent epistemologists and epistemic logicians, who advocate for a correlation between their respective fields of study. We will proceed with a first small step that will consist in adapting one contemporary version of Epistemic Internalism to the framework of Awareness Logic, such that the key (...) concepts in this logic can be sustained by an epistemological view, which, in turn, can work as a theoretical foundation for Awareness Logic. (shrink)

The importance of potential intentions has been demonstrated both in the construction of agent systems and in the formalisation of teamwork behaviour. However, there still lacks an adequate semantics for the notion of potential intentions as introduced by Grosz and Kraus in their SharedPlans framework. In this paper, we give a formal semantics to intentions and potential intentions, drawing upon both the representationalist approach and the accessibility-based approach. The model captures the dynamic relationship among intentions and potential intentions by providing (...) semantic rules and conditions. Also, the model treats norms as a special class of intentional context, and it is shown that norms play a critical role in the dynamics of intentions in multiagent systems. The formal semantics allows us to validate some properties that are widely-accepted for intention attitudes. (shrink)