In abstract argumentation, each argument is regarded as atomic. There is no internal structure to an argument. Also, there is no specification of what is an argument or an attack. They are assumed to be given. This abstract perspective provides many advantages for studying the nature of argumentation, but it does not cover all our needs for understanding argumentation or for building tools for supporting or undertaking argumentation. If we want a more detailed formalization of arguments than is available with (...) abstract argumentation, we can turn to structured argumentation, which is the topic of this special issue of Argument and Computation. In structured argumentation, we assume a formal language for representing knowledge and specifying how arguments and counterarguments can be constructed from that knowledge. An argument is then said to be structured in the sense that normally, the premises and claim of the argument are made explicit, and the relationship between the premises and claim is formally defined (for instance, using logical entailment). In this introduction, we provide a brief overview of the approaches covered in this special issue on structured argumentation. (shrink)

Develops a logical analysis of dialogue in which two or more parties attempt to advance their own interests. It includes a classification of the major types of dialogues and a discussion of several important informal fallacies.

This book identifies 25 argumentation schemes for presumptive reasoning and matches a set of critical questions to each.

This paper summarizes and systematizes recent and ongoing work on non-prioritized belief change, i.e., belief revision in which the new information has no special priority due to its novelty.

In redefining logic, philosophers need to go back to the Aristotelian roots of the subject, to expand the boundaries of the subject to include informal logic and to give up false oppositions between informal and formal logic.

This paper extends earlier work by its authors on formal aspects of the processes of contracting a theory to eliminate a proposition and revising a theory to introduce a proposition. In the course of the earlier work, Gardenfors developed general postulates of a more or less equational nature for such processes, whilst Alchourron and Makinson studied the particular case of contraction functions that are maximal, in the sense of yielding a maximal subset of the theory (or alternatively, of one of (...) its axiomatic bases), that fails to imply the proposition being eliminated. In the present paper, the authors study a broader class, including contraction functions that may be less than maximal. Specifically, they investigate "partial meet contraction functions", which are defined to yield the intersection of some nonempty family of maximal subsets of the theory that fail to imply the proposition being eliminated. Basic properties of these functions are established: it is shown in particular that they satisfy the Gardenfors postulates, and moreover that they are sufficiently general to provide a representation theorem for those postulates. Some special classes of partial meet contraction functions, notably those that are "relational" and "transitively relational", are studied in detail, and their connections with certain "supplementary postulates" of Gardenfors investigated, with a further representation theorem established. (shrink)

Knowledge representation, which lies at the core of artificial intelligence, is concerned with encoding knowledge on computers to enable systems to reason automatically. The aims are to help readers make their computer smarter, handle qualitative and uncertain information, and improve computational tractability.

This paper addresses the issue of the dynamic enforcement of a constraint in an argumentation system. The system consists in (1) an argumentation framework, made up, notably, of a set of arguments...

The field of iterated belief change has focused mainly on revision, with the other main operator of AGM belief change theory, i.e. contraction, receiving relatively little attention. In this paper we extend the Harper Identity from single-step change to define iterated contraction in terms of iterated revision. Specifically, just as the Harper Identity provides a recipe for defining the belief set resulting from contracting A in terms of (i) the initial belief set and (ii) the belief set resulting from revision (...) by ¬A, we look at ways to define the plausibility ordering over worlds resulting from contracting A in terms of (iii) the initial plausibility ordering, and (iv) the plausibility ordering resulting from revision by ¬A. After noting that the most straightforward such extension leads to a trivialisation of the space of permissible orderings, we provide a family of operators for combining plausibility orderings that avoid such a result. These operators are characterised in our domain of interest by a pair of intuitively compelling properties, which turn out to enable the derivation of a number of iterated contraction postulates from postulates for iterated revision. We finish by observing that a salient member of this family allows for the derivation of counterparts for contraction of some well known iterated revision operators, as well as for defining new iterated contraction operators. (shrink)

The paper attacks the widely held view that belief revision theories, as they have been studied in the past two decades, are founded on the Principle of Informational Economy. The principle comes in two versions. According to the first, an agent should, when accepting a new piece of information, aim at a minimal change of his previously held beliefs. If there are different ways to effect the belief change, then the agent should, according to he second version, give up those (...) beliefs that are least entrenched. Although widely proclaimed by belief revision theorists, I argue that both versions of the principle are dogmas that are not (and perhaps should not be) adhered to. I substantiate this claim with two simple mathematical observations, and I defend it against four possible objections that involve contractions, reconstructions, dispositions, and truths. (shrink)

ABSTRACT The major approaches to belief revision and non monotonic reasoning proposed in the literature differ along a number of dimensions, including whether they are “syntax- based” or “semantic-based”, “foundational” or “coherentist”, “consistence-restoring” or “inconsistency-tolerant”. Our contribution towards clarifying the connections between these various approaches is threefold: •We show that the two main approaches to belief revision, the foundations and coherence theories, are mathematically equivalent, thus answering a question left open in [Gar90, Doy92], The distinction between syntax-based approaches to revision (...) and approaches based on (semantic) preferential structures falls along similar lines, and their expressive equivalence is a consequence of this result. •We formally clarify the connection between belief revision and non monotonic reasoning, in a particularly simple way which also throws light on the connection between consistence- restoring and reasoning-from-inconsistency approaches [BDP95]. •As a direct application of the above, we show that Poole's (syntax-based) system of default reasoning and Shoham's preferential semantic for non monotonic reasoning are also expressively equivalent, in that they can represent the same set of non monotonic consequence relations. (shrink)

We show in this paper that the AGM postulates are too weak to ensure the rational preservation of conditional beliefs during belief revision, thus permitting improper responses to sequences of observations. We remedy this weakness by proposing four additional postulates, which are sound relative to a qualitative version of probabilistic conditioning. Contrary to the AGM framework, the proposed postulates characterize belief revision as a process which may depend on elements of an epistemic state that are not necessarily captured by a (...) belief set. We also show that a simple modification to the AGM framework can allow belief revision to be a function of epistemic states. We establish a model-based representation theorem which characterizes the proposed postulates and constrains, in turn, the way in which entrenchment orderings may be transformed under iterated belief revision. (shrink)

This book provides a systematic analysis of many common argumentation schemes and a compendium of 96 schemes. The study of these schemes, or forms of argument that capture stereotypical patterns of human reasoning, is at the core of argumentation research. Surveying all aspects of argumentation schemes from the ground up, the book takes the reader from the elementary exposition in the first chapter to the latest state of the art in the research efforts to formalize and classify the schemes, outlined (...) in the last chapter. It provides a systematic and comprehensive account, with notation suitable for computational applications that increasingly make use of argumentation schemes. (shrink)

There was a long tradition in philosophy according to which good reasoning had to be deductively valid. However, that tradition began to be questioned in the 1960’s, and is now thoroughly discredited. What caused its downfall was the recognition that many familiar kinds of reasoning are not deductively valid, but clearly confer justification on their conclusions. Here are some simple examples.

This book explains how the logic of theory change employs formal models in the investigation of changes in belief states and databases. The topics covered include equivalent characterizations of AGM operations, extended representations of the belief states, change operators not included in the original framework, iterated change, applications of the model, its connections with other formal frameworks, and criticism of the model.

Two systems of belief change based on paraconsistent logics are introduced in this article by means of AGM-like postulates. The first one, AGMp, is defined over any paraconsistent logic which extends classical logic such that the law of excluded middle holds w.r.t. the paraconsistent negation. The second one, AGMo , is specifically designed for paraconsistent logics known as Logics of Formal Inconsistency (LFIs), which have a formal consistency operator that allows to recover all the classical inferences. Besides the three usual (...) operations over belief sets, namely expansion, contraction and revision (which is obtained from contraction by the Levi identity), the underlying paraconsistent logic allows us to define additional operations involving (non-explosive) contradictions. Thus, it is defined external revision (which is obtained from contraction by the reverse Levi identity), consolidation and semi-revision, all of them over belief sets. It is worth noting that the latter operations, introduced by S. Hansson, involve the temporary acceptance of contradictory beliefs, and so they were originally defined only for belief bases. Unlike to previous proposals in the literature, only defined for specific paraconsistent logics, the present approach can be applied to a general class of paraconsistent logics which are supraclassical, thus preserving the spirit of AGM. Moreover, representation theorems w.r.t. constructions based on selection functions are obtained for all the operations. (shrink)

Prioritized bases, i.e., weakly ordered sets of sentences, have been used for specifying an agent’s ‘basic’ or ‘explicit’ beliefs, or alternatively for compactly encoding an agent’s belief state without the claim that the elements of a base are in any sense basic. This paper focuses on the second interpretation and shows how a shifting of priorities in prioritized bases can be used for a simple, constructive and intuitive way of representing a large variety of methods for the change of belief (...) states—methods that have usually been characterized semantically by a system-of-spheres modeling. Among the methods represented are ‘radical’, ‘conservative’ and ‘moderate’ revision, ‘revision by comparison’ in its raising and lowering variants, as well as various constructions for belief expansion and contraction. Importantly, none of these methods makes any use of numbers. (shrink)

Investigates the resolution of contradictions and ambiguous derogations in a code, by means of the imposition of partial orderings.

The Handbook of Formal Argumentation is a community effort aimed at providing a comprehensive and up-to-date view of the state of the art and current trends in the lively research field of formal argumentation. The first volume of the Handbook is organised into five parts, containing nineteen chapters in all, each written by leading experts in the field. The first part provides a general and historical perspective on the field. The second part gives a comprehensive coverage of the argumentation formalisms (...) available in the literature at various levels of abstraction. The third part is devoted to cover some of the many dialogical aspects of argumentation, while the fourth one deals with algorithmic, computational and implementation issues. Finally, the fifth part provides some deeper analyses on the previously introduced topics. The Handbook of Formal Argumentation is an open-ended initiative of which the present volume is the first outcome. Further volumes are planned to cover topics not included in the present one and the initiative is conceived to grow by the support and feeding it receives from the community members. (shrink)

The 1985 paper by Carlos Alchourrón, Peter Gärdenfors, and David Makinson, “On the Logic of Theory Change: Partial Meet Contraction and Revision Functions” was the starting-point of a large and rapidly growing literature that employs formal models in the investigation of changes in belief states and databases. In this review, the first twenty-five years of this development are summarized. The topics covered include equivalent characterizations of AGM operations, extended representations of the belief states, change operators not included in the original (...) framework, iterated change, applications of the model, its connections with other formal frameworks, computatibility of AGM operations, and criticism of the model. (shrink)

ABSTRACT Inspired by legal reasoning, this paper presents a semantics and proof theory of a system for defeasible argumentation. Arguments are expressed in a logic-programming language with both weak and strong negation, conflicts between arguments are decided with the help of priorities on the rules. An important feature of the system is that these priorities are not fixed, but are themselves defeasibly derived as conclusions within the system. Thus debates on the choice between conflicting arguments can also be modelled. The (...) semantics of the system is given with a fixpoint definition, while its proof theory is stated in dialectical style, where a proof takes the form of a dialogue between a proponent and an opponent of an argument: an argument is shown to be justified if the proponent can make the opponent run out of moves in whatever way the opponent attacks. (shrink)

An abstract framework for structured arguments is presented, which instantiates Dung's ('On the Acceptability of Arguments and its Fundamental Role in Nonmonotonic Reasoning, Logic Programming, and n- Person Games', Artificial Intelligence , 77, 321-357) abstract argumentation frameworks. Arguments are defined as inference trees formed by applying two kinds of inference rules: strict and defeasible rules. This naturally leads to three ways of attacking an argument: attacking a premise, attacking a conclusion and attacking an inference. To resolve such attacks, preferences may (...) be used, which leads to three corresponding kinds of defeat: undermining, rebutting and undercutting defeats. The nature of the inference rules, the structure of the logical language on which they operate and the origin of the preferences are, apart from some basic assumptions, left unspecified. The resulting framework integrates work of Pollock, Vreeswijk and others on the structure of arguments and the nature of defeat and extends it in several respects. Various rationality postulates are proved to be satisfied by the framework, and several existing approaches are proved to be a special case of the framework, including assumption-based argumentation and DefLog. (shrink)

Two recent defences of the recovery postulate for contraction of belief sets are analyzed. It is concluded that recovery is defensible as a by-product of a formalization that is idealized in the sense of being simplified for the sake of clarity. However, recovery does not seem to be a required feature of the doxastic behaviour of ideal (perfectly rational) agents. It is reasonable to expect that there should be epistemic residues (remnants of rejected beliefs), but not that these should always (...) suffice to recover all the original beliefs if the discarded belief is reinstated. (shrink)

We present a mathematical approach to defeasible reasoning based on arguments. This approach integrates the notion of specificity introduced by Poole and the theory of warrant presented by Pollock. The main contribution of this paper is a precise, well-defined system which exhibits correct behavior when applied to the benchmark examples in the literature. It aims for usability rather than novelty. We prove that an order relation can be introduced among equivalence classes of arguments under the equi-specificity relation. We also prove (...) a theorem that ensures the termination of the process of finding the justified facts. Two more lemmas define a reduced search space for checking specificity. In order to implement the theoretical ideas, the language is restricted to Horn clauses for the evidential context. The language used to represent defeasible rules has been restricted in a similar way. The authors intend this work to unify the various existing approaches to argument-based defeasible reasoning. (shrink)

A study in the logic of theory change, examining the properties of maxichoice contraction and revision operations.

An agent can usually hold a very large number of beliefs. However, only a small part of these beliefs is used at a time. Efficient operations for belief change should affect the beliefs of the agent locally, that is, the changes should be performed only in the relevant part of the belief state. In this paper we define a local consequence operator that only considers the relevant part of a belief base. This operator is used to define local versions of (...) the operations for belief change. Representation theorems are given for the local operators. (shrink)

We introduce a constructive model of selective belief revision in which it is possible to accept only a part of the input information. A selective revision operator ο is defined by the equality K ο α = K * f(α), where * is an AGM revision operator and f a function, typically with the property ⊢ α → f(α). Axiomatic characterizations are provided for three variants of selective revision.

Develops a concept of revision, akin in spirit to AGM partial meet revision, but in which the postulate of 'success' may fail. The basic idea is to see such an operation as composite, with a pre-processor using a priori considerations to resolve the question of whether to revise, following which another operation revises in a manner that protects the a priori material.

Since the early 1980s, logical theories of belief revision have offered formal methods for the transformation of knowledge bases or “corpora” of data and beliefs. Early models have dealt with unconditional acceptance and integration of potentially belief-contravening pieces of information into the existing corpus. More recently, models of “non-prioritized” revision were proposed that allow the agent rationally to refuse to accept the new information. This paper introduces a refined method for changing beliefs by specifying constraints on the relative plausibility of (...) propositions. Like the earlier belief revision models, the method proposed is a qualitative one, in the sense that no numbers are needed in order to specify the posterior plausibility of the new information. We use reference beliefs in order to determine the degree of entrenchment of the newly accepted piece of information. We provide two kinds of semantics for this idea, give a logical characterization of the new model, study its relation with other operations of belief revision and contraction, and discuss its intuitive strengths and weaknesses. (shrink)

Isaac Levi's new book is concerned with how one can justify changing one's beliefs. The discussion is deeply informed by the belief-doubt model advocated by C. S. Peirce and John Dewey, of which the book provides a substantial analysis. Professor Levi then addresses the conceptual framework of potential changes available to an inquirer. A structural approach to propositional attitudes is proposed, which rejects the conventional view that a propositional attitude involves a relation between an agent and either a linguistic entity (...) or some other intentional object such as a proposition or set of possible worlds. The last two chapters offer an account of change in states of full belief understood as changes in commitments rather than changes in performance; one chapter deals with adding new information to a belief state, the other with giving up information. The book builds upon topics discussed in some of Levi's earlier work. It will be of particular interest to discussion theorists, epistemologists, philosophers of science, computer scientists, and cognitive psychologists. (shrink)