This paper presents a formal account of how to determine the discourse relations between propositions introduced in a text, and the relations between the events they describe. The distinct natural interpretations of texts with similar syntax are explained in terms of defeasible rules. These characterise the effects of causal knowledge and knowledge of language use on interpretation. Patterns of defeasible entailment that are supported by the logic in which the theory is expressed are shown to underly temporal interpretation.

This book provides a critical examination of how the choice of what to believe is represented in the standard model of belief change. In particular the use of possible worlds and infinite remainders as objects of choice is critically examined. Descriptors are introduced as a versatile tool for expressing the success conditions of belief change, addressing both local and global descriptor revision. The book presents dynamic descriptors such as Ramsey descriptors that convey how an agent’s beliefs tend to be changed (...) in response to different inputs. It also explores sentential revision and demonstrates how local and global operations of revision by a sentence can be derived as a special case of descriptor revision. Lastly, the book examines revocation, a generalization of contraction in which a specified sentence is removed in a process that may possibly also involve the addition of some new information to the belief set. (shrink)

According to the Ramsey Test, conditionals reflect changes of beliefs: α > β is accepted in a belief state iff β is accepted in the minimal revision of it that is necessary to accommodate α. Since Gärdenfors’s seminal paper of 1986, a series of impossibility theorems (“triviality theorems”) has seemed to show that the Ramsey test is not a viable analysis of conditionals if it is combined with AGM-type belief revision models. I argue that it is possible to endorse that (...) Ramsey test for conditionals while staying true to the spirit of AGM. A main focus lies on AGM’s condition of Preservation according to which the original belief set should be fully retained after a revision by information that is consistent with it. I use concrete representations of belief states and (iterated) revisions of belief states as semantic models for (nested) conditionals. Among the four most natural qualitative models for iterated belief change, two are identified that indeed allow us to combine the Ramsey test with Preservation in the language containing only flat conditionals of the form α > β. It is shown, however, that Preservation for this simple language enforces a violation of Preservation for nested conditionals of the form α > (β > γ). In such languages, no two belief sets are ordered by strict subset inclusion. I argue that it has been wrong right from the start to expect that Preservation holds in languages containing nested conditionals. (shrink)

Since belief revision deals with the interaction of belief and information over time, branching-time temporal logic seems a natural setting for a theory of belief change. We propose two extensions of a modal logic that, besides the next-time temporal operator, contains a belief operator and an information operator. The first logic is shown to provide an axiomatic characterization of the first six postulates of the AGM theory of belief revision, while the second, stronger, logic provides an axiomatic characterization of the (...) full set of AGM postulates. © 2006 Elsevier B.V. All rights reserved. (shrink)

On the basis of impossibility results on probability, belief revision, and conditionals, it is argued that conditional beliefs differ from beliefs in conditionals qua mental states. Once this is established, it will be pointed out in what sense conditional beliefs are still conditional, even though they may lack conditional contents, and why it is permissible to still regard them as beliefs, although they are not beliefs in conditionals. Along the way, the main logical, dispositional, representational, and normative properties of conditional (...) beliefs are studied, and it is explained how the failure of not distinguishing conditional beliefs from beliefs in conditionals can lead philosophical and empirical theories astray. (shrink)

The starting point of this work is the gap between two distinct traditions in information engineering: knowledge representation and data - driven modelling. The first tradition emphasizes logic as a tool for representing beliefs held by an agent. The second tradition claims that the main source of knowledge is made of observed data, and generally does not use logic as a modelling tool. However, the emergence of fuzzy logic has blurred the boundaries between these two traditions by putting forward fuzzy (...) rules as a Janus-faced tool that may represent knowledge, as well as approximate non-linear functions representing data. This paper lays bare logical foundations of data - driven reasoning whereby a set of formulas is understood as a set of observed facts rather than a set of beliefs. Several representation frameworks are considered from this point of view: classical logic, possibility theory, belief functions, epistemic logic, fuzzy rule-based systems. Mamdani's fuzzy rules are recovered as belonging to the data - driven view. In possibility theory a third set-function, different from possibility and necessity plays a key role in the data - driven view, and corresponds to a particular modality in epistemic logic. A bi-modal logic system is presented which handles both beliefs and observations, and for which a completeness theorem is given. Lastly, our results may shed new light in deontic logic and allow for a distinction between explicit and implicit permission that standard deontic modal logics do not often emphasize. (shrink)

The temporal updating of an agent’s beliefs in response to a flow of information is modeled in a simple modal logic that, for every date t, contains a normal belief operator B t and a non-normal information operator I t which is analogous to the ‘only knowing’ operator discussed in the computer science literature. Soundness and completeness of the logic are proved and the relationship between the proposed logic, the AGM theory of belief revision and the notion of plausibility is (...) discussed. (shrink)

Diversity of agents occurs naturally in epistemic logic, and dynamic logics of information update and belief revision. In this paper we provide a systematic discussion of different sources of diversity, such as introspection ability, powers of observation, memory capacity, and revision policies, and we show how these can be encoded in dynamic epistemic logics allowing for individual variation among agents. Next, we explore the interaction of diverse agents by looking at some concrete scenarios of communication and learning, and we propose (...) a logical methodology to deal with these as well. We conclude with some further questions on the logic of diversity and interaction. (shrink)

Normic Laws and the Significance of Nonmonotonic Reasoning for Philosophy of Science. Normic laws have the form ‘if A then normally B’. They have been discovered in the explanation debate, but were considered as empirically vacuous (§1). I argue that the prototypical (or ideal) normality of normic laws implies statistical normality (§2), whence normic laws have empirical content. In §3–4 I explain why reasoning from normic laws is nonmonotonic, and why the understanding of the individual case is so important here. (...) After sketching some foundations of nonmonotonic reasoning as developed by AI-researchers (§5), Iargue that normic laws are also the best way to understand ceteris paribus laws (§6). §7 deals with the difference between physical and non-physical disciplines and §9 with the difference between normicity and approximation. In §8 it is shown how nonmonotonic reasoning provides a new understanding of the protection of theories against falsification by auxiliary hypotheses. §10, finally, gives a system- and evolution-theoretical explanation of the deeper reason for the omnipresence of normic laws in practice and science, and forthe connection between ideal and statistical normality. (shrink)

Performing an inference involves irreducibly dynamic cognitive procedures. The article proposes that a non-associative information frame, corresponding to a residuated pogroupoid, underpins the information structure involved. The argument proceeds by expounding the informational turn in logic, before outlining the cognitive actions at work in deductive inference. The structural rules of Weakening, Contraction, Commutation, and Association are rejected on the grounds that they cause us to lose track of the information flow in inferential procedures. By taking the operation of information application (...) as the primary operation, the fusion connective is retained, with commutative failure generating a double implication. The other connectives are rejected. (shrink)

Classical modal logics, based on the neighborhood semantics of Scott and Montague, provide a generalization of the familiar normal systems based on Kripke semantics. This paper defines AGM revision operators on several first-order monotonic modal correspondents, where each first-order correspondence language is defined by Marc Pauly’s version of the van Benthem characterization theorem for monotone modal logic. A revision problem expressed in a monotone modal system is translated into first-order logic, the revision is performed, and the new belief set is (...) translated back to the original modal system. An example is provided for the logic of Risky Knowledge that uses modal AGM contraction to construct counter-factual evidence sets in order to investigate robustness of a probability assignment given some evidence set. A proof of correctness is given. (shrink)

We present a neighbourhood-style semantic framework for modal epistemic logic modelling agents who process information using relevant logic. The distinguishing feature of the framework in comparison to relevant modal logic is that the environment the agent is situated in is assumed to be a classical possible world. This framework generates two-layered logics combining classical logic on the propositional level with relevant logic in the scope of modal operators. Our main technical result is a general soundness and completeness theorem.

We extend our general approach to characterizing information to multi-agent systems. In particular, we provide a formal description of an agent''s knowledge containing exactly the information conveyed by some (honest) formula . Only knowing is important for dynamic agent systems in two ways. First of all, one wants to compare different states of knowledge of an agent and, secondly, for agent a''s decisions, it may be relevant that (he knows that) agent b does not know more than . There are (...) three ways to study the question whether a formula can be interpreted as minimal information. The first method is semantic and inspects minimal models for (with respect to some information order on states). The second one is syntactic and searches for stable expansions, minimal with respect to some language *. The third method is a deductive test, known as the disjunction property. We present a condition under which the three methods are equivalent. Then, we show how to construct the order by collecting layered orders. Focusing on the multi-agent case we identify languages * for various orders , and show how they yield different notions of honesty for different multi-modal systems. We then provide several tools for studying honesty types and illustrate their usefulness on a number of examples, for three modal systems of particular interest. Finally, we relate the different notions of minimal knowledge, and describe possible patterns of honesty for these systems. (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)

A recurring issue in any formal model representing agents' (changing) informational attitudes is how to account for the fact that the agents are limited in their access to the available inference steps, possible observations and available messages. This may be because the agents are not logically omniscient and so do not have unlimited reasoning ability. But it can also be because the agents are following a predefined protocol that explicitly limits statements available for observation and/or communication. Within the broad literature (...) on epistemic logic, there are a variety of accounts that make precise a notion of an agent's "limited access" (for example, Awareness Logics, Justification Logics, and Inference Logics). This paper interprets the agents' access set of formulas as a constraint on the agents' information gathering process limiting which formulas can be observed. (shrink)

In the literature on Non-Monotonic Logics, many examples of defeasible deductions infer that an arbitrarily chosen individual in a given set has the properties that we consider as “typical” for the elements of that set. In the paper we provide a logical framework, based on first-order logic, suitable for this kind of inferences. The main features of our approach are: 1) typicality of a given property for the individuals in a given set is represented by means of a binary determiner, (...) 2) individual constants are evaluated on sets of individuals, so that a “range of uncertainty” is ascribed to them, 3) the adopted formalism and semantics allow formulas that adequately represent assertions like “it is highly plausible that the individual c has the property P”, and 4) the formal conditions under which “c has the property P” can consistently be inferred from the above assertion are determined, 5) non-monotonicity is achieved by changing the evaluation of the individual constants. In Appendices A, B and C, we provide a sound complete axiom system for the logic considered in the paper. (shrink)