This paper places formal learning theory in a broader philosophical context and provides a glimpse of what the philosophy of induction looks like from a learning-theoretic point of view. Formal learning theory is compared with other standard approaches to the philosophy of induction. Thereafter, we present some results and examples indicating its unique character and philosophical interest, with special attention to its unified perspective on inductive uncertainty and uncomputability.

The connection between the probabilities of conditionals and the corresponding conditional probabilities has long been explored in the philosophical literature, but its implementation faces both technical obstacles and objections on empirical grounds. In this paper I ?rst outline the motivation for the probabilistic turn and Lewis’ triviality results, which stand in the way of what would seem to be its most straightforward implementation. I then focus on Richard Jeffrey’s ’random-variable’ approach, which circumvents these problems by giving up the notion that (...) conditionals denote propositions in the usual sense. Even so, however, the random-variable approach makes counterintuitive predictions in simple cases of embedded conditionals. I propose to address this problem by enriching the model with an explicit representation of causal dependencies. The addition of such causal information not only remedies the shortcomings of Jeffrey’s conditional, but also opens up the possibility of a uni?ed probabilistic account of indicative and counterfactual 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)

The Meno problem, asking for the surplus value of knowledge beyond the value of true justified belief, was recently much treated within reliabilist and virtue epistemologies. The answers from formal epistemology, by contrast, are quite poor. This paper attempts to improve the score of formal epistemology by precisely explicating Timothy Williamson's suggestion that ‘present knowledge is less vulnerable than mere present true belief to rational undermining by future evidence’. It does so by combining Nozick's sensitivity analysis of knowledge with Spohn's (...) fact‐asserting epistemic interpretation of conditionals. Accordingly, the surplus value of knowledge lies in a specific kind of stability of knowledge, which differs, though, from that claimed by other so‐called stability analyses of knowledge. (shrink)

In this paper I construct a system of semantics for classical and intuitionistic propositional logic based on epistemic norms governing belief expansion. Working in the AGM-framework of belief change, I give a generalisation of Gärdenfors’ notion of belief systems which can be defined without reference to a logical consequence operator by using a version of the Ramsey Test. These belief expansion systems can then be used to define epistemic models which are sound and complete for either classical or intuitionistic propositional (...) logic depending on which of the two notions of epistemic validity, identified by Levi and Arló-Costa, is used. Finally, I offer a discussion on how these results can be understood as providing a model theory within the framework of logical expressivism. (shrink)

Conditional statements are ubiquitous, from promises and threats to reasoning and decision making. By now, logicians have studied them from many different angles, both semantic and proof-theoretic. This paper suggests two more perspectives on the meaning of conditionals, one dynamic and one geometric, that may throw yet more light on a familiar and yet in some ways surprisingly elusive and many-faceted notion.1.

Theoria, Volume 88, Issue 3, Page 494-528, June 2022.

This paper expounds a simple and non-trivial Ramsey Test. Drawing on the work of Peter Gärdenfors, it aims to help establish an epistemic alternative to the semantics of variably strict conditionals by Robert Stalnaker (in: Rescher (ed), Studies in logical theory, Blackwell, Oxford, 1968) and David Lewis (Counterfactuals, Blackwell, Oxford, 1973). The novelty of the present contribution lies in considering the framework of Preferred Subtheories as model of belief change upon which conditionals are defined. The resulting semantics avoids triviality in (...) the sense that a major premise of the proof of Gärdenfors’ triviality theorem is violated. (shrink)

According to Stalnaker’s Thesis, the probability of a conditional is the conditional probability. Under some mild conditions, the thesis trivialises probabilities and conditionals, as initially shown by David Lewis. This article asks the following question: does still lead to triviality, if the probability function in is replaced by a probability-like function? The article considers plausibility functions, in the sense of Friedman and Halpern, which additionally mimic probabilistic additivity and conditionalisation. These quasi probabilities comprise Friedman–Halpern’s conditional plausibility spaces, as well as (...) other known representations of conditional doxastic states. The paper proves Lewis’ triviality for quasi probabilities and discusses how this has implications for three other prominent strategies to avoid Lewis’ triviality: Adams’ thesis, where the probability function on the left in is replaced by a probability-like function, abandoning conditionalisation, where probability conditionalisation on the right in is replaced by another propositional update procedure and the approximation thesis, where equality in is replaced by approximation. The paper also shows that Lewis’ triviality result is really about ‘additiveness’ and ‘conditionality’. (shrink)

Orthodox Bayesianism endorses revising by conditionalization. This paper investigates the zero-raising problem, or equivalently the certainty-dropping problem of orthodox Bayesianism: previously neglected possibilities remain neglected, although the new evidence might suggest otherwise. Yet, one may want to model open-minded agents, that is, agents capable of raising previously neglected possibilities. Different reasons can be given for open-mindedness, one of which is fallibilism. The paper proposes a family of open-minded propositional revisions depending on a parameter ϵ. The basic idea is this: first (...) extend the prior to the newly suggested possibilities by mixing the prior with the uniform probability on these possibilities, then conditionalize. This may put the agent back on the right track when her beliefs or evidence happen to be false. The paper justifies this family of equivocal epsilon-conditionalizations as minimal non-biased open-minded modifications of conditionalization. Several variations are discussed, such as mixing with an ad hoc or silent prior instead of the uniform prior, and a generalization to probabilistic information is given. The approach is compared to other accounts, such as Jeffrey’s Bayesianism, Gärdenfors’s probabilistic revision, maximizing entropy, and minimal revision. _1_ Introduction _2_ Downsides of Certainty Conservation _3_ Why Raise Zeros? _3.1_ Accuracy defects _3.2_ Fallibilism and dissolutions _3.3_ Weak fallibilism and partial solutions _4_ Epsilon-Conditionalization _4.1_ Definitions _4.2_ Revision types and information assumptions _4.3_ Epsilon interpretation and flavours _5_ Justifications _5.1_ Open-minded orthodox Bayesianism _5.2_ Minimal revision _5.3_ Transitivity _6_ Conclusion Appendix. (shrink)

A realist approach to learning is what I propose here. This is based on a non-epistemic dimension whose presence is a necessary assumption for a concept of learning of a life-world as complementary to learning within a life-world. I develop my approach in opposition to Jürgen Habermas' pragmatic approach, which seems to lack of something from a realist point of view.

We investigate the research programme of dynamic doxastic logic (DDL) and analyze its underlying methodology. The Ramsey test for conditionals is used to characterize the logical and philosophical differences between two paradigmatic systems, AGM and KGM, which we develop and compare axiomatically and semantically. The importance of Gärdenfors’s impossibility result on the Ramsey test is highlighted by a comparison with Arrow’s impossibility result on social choice. We end with an outlook on the prospects and the future of DDL.

Implicatures are described as particular forms reasoning from best explanation, in which the para-digm of possible explanations consists of the possible semantic interpretations of a sentence or a word. The need for explanation will be shown to be triggered by conflicts between presumptions, namely hearer’s dialogical expectations and the presumptive sentence meaning. What counts as the best explanation can be established on the grounds of hierarchies of presumptions, dependent on dialogue types and interlocutors’ culture.

This essay develops a joint theory of rational (all-or-nothing) belief and degrees of belief. The theory is based on three assumptions: the logical closure of rational belief; the axioms of probability for rational degrees of belief; and the so-called Lockean thesis, in which the concepts of rational belief and rational degree of belief figure simultaneously. In spite of what is commonly believed, this essay will show that this combination of principles is satisfiable (and indeed nontrivially so) and that the principles (...) are jointly satisfied if and only if rational belief is equivalent to the assignment of a stably high rational degree of belief. Although the logical closure of belief and the Lockean thesis are attractive postulates in themselves, initially this may seem like a formal “curiosity”; however, as will be argued in the rest of the essay, a very reasonable theory of rational belief can be built around these principles that is not ad hoc and that has various philosophical features that are plausible independently. In particular, this essay shows that the theory allows for a solution to the Lottery Paradox, and it has nice applications to formal epistemology. The price that is to be paid for this theory is a strong dependency of belief on the context, where a context involves both the agent's degree of belief function and the partitioning or individuation of the underlying possibilities. But as this essay argues, that price seems to be affordable. (shrink)

ABSTRACT We consider evolution of knowledge bases caused by a sequence of basic steps of acquisition of a new information, either consistent or inconsistent with the original system. To make this process comply with the Principe of Minimal Change, a special evidence metric is introduced for measuring distance between states of knowledge. Then a novel semantics of knowledge bases is developed suggested by the heuristics of weighted maximally consistent subsets. The latter is efficiently applied to the processes of consistent and (...) inconsistent acquisition of knowledge, belief revision and contraction. (shrink)

We give a condensed survey of recent research on generalized quantifiers in logic, linguistics and computer science, under the following headings: Logical definability and expressive power, Polyadic quantifiers and linguistic definability, Weak semantics and axiomatizability, Computational semantics, Quantifiers in dynamic settings, Quantifiers and modal logic, Proof theory of generalized quantifiers.

In this paper we investigate three approaches to iterated contraction, namely: the Moderate (or Priority) contraction, the Natural (or Conservative) contraction, and the Lexicographic contraction. We characterise these three contraction functions using certain, arguably plausible, properties of an iterated contraction function. While we provide the characterisation of the first two contraction operations using rationality postulates of the standard variety for iterated contraction, we found doing the same for the Lexicographic contraction more challenging. We provide its characterisation using a variation of (...) Epistemic ranking function instead. (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)

Review of Olsson, Erik J. and Enqvist, Sebastian , Belief Revision meets Philosophy of Science.

The principle of belief persistence, or conservativity principle, states that ’\Nhen changing beliefs in response to new evidence, you should continue to believe as many of the old beliefs as possible' (Harman, 1986, p. 46). In particular, this means that if an individual gets new information, she has to accommodate it in her new belief set (the set of propositions she believes), and, if the new information is not inconsistent with the old belief set, then (1) the individual has to (...) maintain all the beliefs she previously had and (2) the change should be minimal in the sense that every proposition in the new belief set must be deducible from the union of the old belief set and the new information (see, e.g., Gardenfors, 1988; Stalnaker, 1984). We focus on this minimal notion of belief persistence and characterize it both semantically and syntactically. A ’possible world' semantic formalization of the principle easily comes to mind. The set of all the propositions that the individual believes corresponds to the set of states of the world that she considers possible and is a subset of the set of states that are not ruled out by the individual's information (or knowledge). It is required that, if the individual considers a state possible and her new information does not exclude this state, then she continue to consider it possible. Furthermore, if the individual regards a particular state as impossible, then she should continue to regard it as impossible unless her new information excludes all the states that she previously regarded as possible. This is closely related to the.. (shrink)

A model of inductive inquiry is defined within the context of first‐order logic. The model conceives of inquiry as a game between Nature and a scientist. To begin the game, a nonlogical vocabulary is agreed upon by the two players, along with a partition of a class of countable structures for that vocabulary. Next, Nature secretly chooses one structure from some cell of the partition. She then presents the scientist with a sequence of facts about the chosen structure. With each (...) new datum the scientist announces a guess about the cell to which the chosen structure belongs. To succeed in his or her inquiry, the scientist’s successive conjectures must be correct all but finitely often, that is, the conjectures must converge in the limit to the correct cell. Different kinds of scientists can be investigated within this framework. At opposite ends of the spectrum are dumb scientists that rely on the strategy of “induction by enumeration,” and smart scientists that rely on an operator of belief revision. We report some results about the scope and limits of these two inductive strategies. (shrink)

This paper analyzes the notion of a minimal belief change that incorporates new information. I apply the fundamental decision-theoretic principle of Pareto-optimality to derive a notion of minimal belief change, for two different representations of belief: First, for beliefs represented by a theory – a deductively closed set of sentences or propositions – and second for beliefs represented by an axiomatic base for a theory. Three postulates exactly characterize Pareto-minimal revisions of theories, yielding a weaker set of constraints than the (...) standard AGM postulates. The Levi identity characterizes Pareto-minimal revisions of belief bases: a change of belief base is Pareto-minimal if and only if the change satisfies the Levi identity (for “maxichoice” contraction operators). Thus for belief bases, Pareto-minimality imposes constraints that the AGM postulates do not. The Ramsey test is a well-known way of establishing connections between belief revision postulates and axioms for conditionals (“if p, then q”). Pareto-minimal theory change corresponds exactly to three characteristic axioms of counterfactual systems: a theory revision operator that satisfies the Ramsey test validates these axioms if and only if the revision operator is Pareto-minimal. (shrink)

An essay review of Richard Johns "A Theory of Physical Probability" (University of Toronto Press, 2002). Forthcoming in Studies in History and Philosophy of Science.

Isaac Levi has claimed that our reliance on the testimony of others, and on the testimony of the senses, commonly produces inconsistency in our set of full beliefs. This happens if what is reported is inconsistent with what we believe to be the case. Drawing on a conception of the role of beliefs in inquiry going back to Dewey, Levi has maintained that the inconsistent belief corpus is a state of ``epistemic hell'': it is useless as a basis for inquiry (...) and deliberation. As he has also noticed, the compatibility of these two elements of his pragmatist epistemology could be called into question. For if inconsistency means hell, how can it ever be rational to enter that state, and on what basis could we attempt to regain consistency? Levi, nonetheless, has tried to show that the conflict is only apparent and that no changes of his theory are necessary. In the main part of the paper I argue, by contrast, that his attempts to reconcile these components of his view are unsuccessful.The conflict is real andthus presents a genuine threat to Deweyan pragmatism, as understood by Levi. After an attempt to pinpoint exactly where the source of the problem lies, I explore some possibilities for how to come to grips with it. I conclude that Levi can keep his fundamental thesis concerning the role of beliefs in inquiry and deliberation, provided that he (i) gives up the view that the agent can legitimately escape from inconsistency, and (ii) modifies his account of prediction alias deliberate expansion by acknowledging a third desideratum, besides probability and informational value, namely, not to cause permanent breakdown further down the line of inquiry. The result is a position which is more similar to Peter Gärdenfors's than is Levi's original theory, while retaining the basic insights of the latter. (shrink)

We show in this paper that some expressions indicating source of evidence are part of propositional content and are best analyzed as special kind of epistemic modal. Our evidence comes from the Japanese evidential system. We consider six evidentials in Japanese, showing that they can be embedded in conditionals and under modals and that their properties with respect to modal subordination are similar to those of ordinary modals. We show that these facts are difficult for existing theories of evidentials, which (...) assign evidentials necessarily widest scope, to explain. We then provide an analysis using a logical system designed to account for evidential reasoning; this logic is the first developed system of probabilistic dynamic predicate logic. This analysis is shown to account for the data we provide that is problematic for other theories. (shrink)

The postulate of Recovery, among the six postulates for theory contraction, formulated and studied by Alchourrón, Gärdenfors and Makinson is the one that has provoked most controversy. In this article we construct withdrawal functions that do not satisfy Recovery, but try to preserve minimal change, and relate these withdrawal functions with the AGM contraction functions.

Belief fusion, instead of AGM belief revision, was first proposed to solve the problem of inconsistency, that arised from repetitive application of the operation when agents' knowledge were amalgamated. In the preceding work of Maynard-Reid II and Shoham, the fusion operator is applied to belief states, which is total preorders over possible worlds which is based on the semantics of belief revision. Moreover, they introduced the pedigreed belief state, which represented multiple sources of belief states, ordered by a credibility ranking. (...) However in the theory, all the sources must be totally ordered and thus applicable area is quite restrictive. In this paper, we realize the fusion operator of multiple agents for partially ordered sources. When we consider such a partial ranking over sources, there is no need to restrict that each agent has total preorders over possible worlds. The preferential model, based on the semantics on nonmonotonic reasoning, allows each agent to have strict partial orders over possible worlds. Especially, such an order is called a preferential relation, that prescribes a world is more plausible than the other. Therefore, we introduce an operation which combines multiple preferential relations of agents. In addition, we show that our operation can properly include the ordinary belief fusion. (shrink)

In this paper, the contributions to the account of meta-induction (Schurz 2019) collected in this volume are critically discussed and thereby, new insights are developed. How broad and expandable the program of meta-induction is can be learned from Ortner’s contribution. New insights about the transition from the a priori justification of meta-induction to the a posteriori justification of object-induction emerge from the reflection of Shogenji’s paper. How meta-induction may be applied also to religious prophecies and that their meta-inductive justification does (...) not fail for a priori reasons but because of missing evidence for predictive success is learned from the discussion of Pitts’ contribution. That meta-induction does not rely on a particular prior distribution, while the no free lunch theorem depends implicitly on a uniform prior, is the major conclusion drawn from the discussion of Wolpert’s article. How the problem of induction is treated in different versions of the Bayesian account is learned from the discussion of Willliamson’s paper. That meta-induction can also be employed for abduction, and that abductive theory-revision can offer meta-inductive aggregation methods is a new insight emerging from the reflection of Aliseda’s contribution. (shrink)

In an earlier paper [Rational choice and AGM belief revision, _Artificial Intelligence_, 2009] a correspondence was established between the set-theoretic structures of revealed-preference theory (developed in economics) and the syntactic belief revision functions of the AGM theory (developed in philosophy and computer science). In this paper we extend the re-interpretation of those structures in terms of one-shot belief revision by relating them to the trichotomous attitude towards information studied in Garapa (Rev Symb Logic, 1–21, 2020) where information may be either (...) (1) fully accepted or (2) rejected or (3) taken seriously but not fully accepted. We begin by introducing the syntactic notion of _filtered belief revision_ and providing a characterization of it in terms of a mixture of both AGM revision and contraction. We then establish a correspondence between the proposed notion of filtered belief revision and the above-mentioned set-theoretic structures, interpreted as semantic _partial_ belief revision structures. We also provide an interpretation of the trichotomous attitude towards information in terms of the degree of implausibility of the information. (shrink)

This paper aims at comparing and relating belief revision and argumentation as approaches to model reasoning processes. Referring to some prominent literature references in both fields, we will discuss their (implicit or explicit) assumptions on the modeled processes and hence commonalities and differences in the forms of reasoning they are suitable to deal with. The intended contribution is on one hand assessing the (not fully explored yet) relationships between two lively research fields in the broad area of defeasible reasoning and (...) on the other hand pointing out open issues and potential directions for future research. (shrink)

At first glance, what scientific progress means seems to be a quickly answered question. It is not easy to think of the sciences without progress; sciences and the notion of progress seem identical in general. Describing the nature of scientific progress is an important task that will have practical and theoretical consequences. The approach, which argues that the background on which sciences are based does not have a historical or cultural character following the positivist interpretation, accepts sciences as testing the (...) validity of observation and experiment data to a large extent. On the other hand, the tendency that emphasizes that the complex functioning of the history of science has an indelible mark on scientific theories prefers to build sciences on a historical and social basis. How both major approaches ground the idea of scientific progress profoundly affects both our understanding of the nature of scientific knowledge and the way we do science. This paper aims to evaluate scientific progress based on the views of prominent philosophers of science in the twentieth century. (shrink)

Various semantics for studying the square of opposition have been proposed recently. So far, only [14] studied a probabilistic version of the square where the sentences were interpreted by (negated) defaults. We extend this work by interpreting sentences by imprecise (set-valued) probability assessments on a sequence of conditional events. We introduce the acceptability of a sentence within coherence-based probability theory. We analyze the relations of the square in terms of acceptability and show how to construct probabilistic versions of the square (...) of opposition by forming suitable tripartitions. Finally, as an application, we present a new square involving generalized quantifiers. (shrink)

In Bayesian belief revision a Bayesian agent revises his prior belief by conditionalizing the prior on some evidence using Bayes’ rule. We define a hierarchy of modal logics that capture the logical features of Bayesian belief revision. Elements in the hierarchy are distinguished by the cardinality of the set of elementary propositions on which the agent’s prior is defined. Inclusions among the modal logics in the hierarchy are determined. By linking the modal logics in the hierarchy to the strongest modal (...) companion of Medvedev’s logic of finite problems it is shown that the modal logic of belief revision determined by probabilities on a finite set of elementary propositions is not finitely axiomatizable. (shrink)

I propose an account of indicative conditionals that combines features of minimal change semantics and information semantics. As in information semantics, conditionals are interpreted relative to an information state in accordance with the Ramsey test idea: “if p then q” is supported at a state s iff q is supported at the hypothetical state s[p] obtained by restricting s to the p-worlds. However, information states are not modeled as simple sets of worlds, but by means of a Lewisian system of (...) spheres. Worlds in the inner sphere are considered possible; worlds outside of it are ruled out, but to different degrees. In this way, even when a state supports “not p”, it is still possible to suppose p consistently. I argue that this account does better than its predecessors with respect to a set of desiderata concerning inferences with conditionals. In particular, it captures three important facts: that a conditional is logically independent from its antecedent; that a sequence of antecedents behaves like a single conjunctive antecedent ; and that conditionals restrict the quantification domain of epistemic modals. I also discuss two ways to construe the role of a premise, and propose a generalized notion of entailment that keeps the two apart. (shrink)

This position paper advocates combining formal epistemology and the new paradigm psychology of reasoning in the studies of conditionals and reasoning with uncertainty. The new paradigm psychology of reasoning is characterized by the use of probability theory as a rationality framework instead of classical logic, used by more traditional approaches to the psychology of reasoning. This paper presents a new interdisciplinary research program which involves both formal and experimental work. To illustrate the program, the paper discusses recent work on the (...) paradoxes of the material conditional, nonmonotonic reasoning, and Adams’ Thesis. It also identifies the issue of updating on conditionals as an area which seems to call for a combined formal and empirical approach. (shrink)

Richard Bradley has initiated a new debate, with Brian Hill and Jake Chandler as further participants, about the implications of a number of so-called triviality results surrounding the Ramsey test for conditionals. I comment on this debate and argue that ‘Inclusion’ and ‘Preservation’, which were originally introduced as postulates for the rational revision of factual beliefs, have little to recommend them in the first place when extended to languages containing conditionals. I question the philosophical method of postulation that was applied (...) in the new debate, and instead base my arguments on explicit representations of belief states and canonical constructions of belief state revisions. (shrink)

The well known AGM framework for belief revision has recently been extended to include a model of the research agenda of the agent, i.e. a set of questions to which the agent wishes to find answers (Olsson & Westlund in Erkenntnis , 65 , 165–183, 2006 ). The resulting model has later come to be called interrogative belief revision . While belief revision has been studied extensively from the point of view of modal logic, so far interrogative belief revision has (...) only been dealt with in the metalanguage approach in which AGM was originally presented. In this paper, I show how to model interrogative belief revision in a modal object language using a class of operators for questions. In particular, the solution I propose will be shown to capture the notion of K-truncation , a method for agenda update in the case of expansion constructed by Olsson & Westlund. Two case studies are conducted: first, an interrogative extension of Krister Segerberg’s system DDL, and then a similar extension of Giacomo Bonanno’s modal logic for belief revision. Sound and complete axioms will be provided for both of the resulting logics. (shrink)

The Ramseyan thesis that the probability of an indicative conditional is equal to the corresponding conditional probability of its consequent given its antecedent is both widely confirmed and subject to attested counterexamples (e.g., McGee 2000, Kaufmann 2004). This raises several puzzling questions. For instance, why are there interpretations of conditionals that violate this Ramseyan thesis in certain contexts, and why are they otherwise very rare? In this paper, I raise some challenges to Stefan Kaufmann's account of why the Ramseyan thesis (...) sometimes fails, and motivate my own theory. On my theory, the proposition expressed by an indicative conditional is partially determined by a background partition, and hence its probability depends on the choice of such a partition. I hold that this background partition is contextually determined, and in certain conditions is set by a salient question under discussion in the context. I show how the resulting theory offers compelling answers to the puzzling questions raised by failures of the Ramseyan thesis. (shrink)

In this paper we investigate how to represent and reason about legal abrogations and annulments in Defeasible Logic. We examine some options that embed in this setting, and in similar rule-based systems, ideas from belief and base revision. In both cases, our conclusion is negative, which suggests to adopt a different logical model. This model expresses temporal aspects of legal rules, and distinguishes between two main timelines, one internal to a given temporal version of the legal system, and another relative (...) to how the legal system evolves over time. Accordingly, we propose a temporal extension of Defeasible Logic suitable to express this model and to capture abrogation and annulment. We show that the proposed framework overcomes the difficulties discussed in regard to belief and base revision, and is sufficiently flexible to represent many of the subtleties characterizing legal abrogations and annulments. (shrink)

Belief revision theory and philosophy of science both aspire to shed light on the dynamics of knowledge – on how our view of the world changes in the light of new evidence. Yet these two areas of research have long seemed strangely detached from each other, as witnessed by the small number of cross-references and researchers working in both domains. One may speculate as to what has brought about this surprising, and perhaps unfortunate, state of affairs. One factor may be (...) that while belief revision theory has traditionally been pursued in a bottom- up manner, focusing on the endeavors of single inquirers, philosophers of science, inspired by logical empiricism, have tended to be more interested in science as a multi-agent or agent-independent phenomenon. (shrink)