The primary aim of this chapter is to explain the nature of evidential reasoning, the characteristic difficulties encountered, and the tools to address these difficulties. Our focus is on evidential reasoning in criminal cases. There is an extensive scholarly literature on these topics, and it is a secondary aim of the chapter to provide readers the means to find their way in historical and ongoing debates.

In this paper, the Carneades argumentation system is extended to represent a procedural view of inquiry in which evidence is marshalled to support or defeat claims to knowledge. The model is a sequence of moves in a collaborative group inquiry in which parties take turns making assertions about what is known or not known, putting forward evidence to support them, and subjecting these moves to criticisms. It is shown how this model of evaluating evidence in an inquiry is based on (...) a defeasible logic using forms of argument that admit exceptions. It is contended that reasoning from absence of knowledge is as important to inquiry as positive reasoning from evidence to knowledge. The philosophical conflict between this view of reasoning about knowledge and the true-belief-plus view is explored by airing objections and replies on both sides. (shrink)

Dispute types can roughly be divided in two classes. One class in whichthe notion of justification is fundamental, and one in which thenotion of opposition is fundamental. Further, for every singledispute type there exist various types of protocols to conduct such adispute. Some protocols permit local search (a process in which oneis allowed to justify claims partially, with the possibility to extendjustifications on request later), while other protocols rely on globalsearch (a process in which only entire arguments count as justifications).This (...) paper integrates the two above-mentioned types of dispute withthe use of a protocol that permits local search. The locality aspect isrelatively new to computer scientists, while the detailed computationalelaboration of the approach is relatively new to philosophical logicians.The proposed protocol is demonstrated with the help of eight benchmarks.These benchmarks are centered around the problem that co-concludingarguments sometimes accrue, and sometimes do not. (shrink)

Information technology is so ubiquitous and AI’s progress so inspiring that also legal professionals experience its benefits and have high expectations. At the same time, the powers of AI have been rising so strongly that it is no longer obvious that AI applications (whether in the law or elsewhere) help promoting a good society; in fact they are sometimes harmful. Hence many argue that safeguards are needed for AI to be trustworthy, social, responsible, humane, ethical. In short: AI should be (...) good for us. But how to establish proper safeguards for AI? One strong answer readily available is: consider the problems and solutions studied in AI & Law. AI & Law has worked on the design of social, explainable, responsible AI aligned with human values for decades already, AI & Law addresses the hardest problems across the breadth of AI (in reasoning, knowledge, learning and language), and AI & Law inspires new solutions (argumentation, schemes and norms, rules and cases, interpretation). It is argued that the study of AI as Law supports the development of an AI that is good for us, making AI & Law more relevant than ever. (shrink)

In some cases one is provided with inconsistent information and has to reason about various consistent scenarios contained within that information. Our goal is to argue that filtered paraconsistent logics are not the right tool to handle such cases and that the problems generalise to a large class of paraconsistent logics. A wide class of paraconsistent logics is obtained by filtration: adding conditions to the classical consequence operation . We start by surveying the most promising candidates and comparing their strengths. (...) Then we discuss the mainstream views on how non-classical logics should be chosen for an application and argue that none of these allows us to choose any of the filtered logics for action-guiding reasoning with inconsistent information, because such reasoning has to start with the selection of possible scenarios – and such a.. (shrink)

In this paper we show that any reasoning process in which conclusions can be both fallible and corrigible can be formalized in terms of two approaches: (i) syntactically, with the use of defeasible reasoning, according to which reasoning consists in the construction and assessment of arguments for and against a given claim, and (ii) semantically, with the use of partial structures, which allow for the representation of less than conclusive information. We are particularly interested in the formalization of scientific reasoning, (...) along the lines traced by Lakatos’ methodology of scientific research programs. We show how current debates in cosmology could be put into this framework, shedding light on a very controversial topic. (shrink)

In economically meaningful interactions negotiations are particularly important because they allow agents to improve their information about the environment and even to change accordingly their own characteristics. In each step of a negotiation an agent has to emit a message. This message conveys information about her preferences and endowments. Given that the information she uses to decide which message to emit comes from beliefs generated in previous stages of the negotiation, she has to cope with the uncertainty associated with them. (...) The assessment of the states of the world also evolves during the negotiation. In this paper we analyze the intertwined dynamics of beliefs and decision, in order to determine conditions on the agents that allow them to reach agreements. The framework for decision making we consider here is based on defeasible evaluation of possibilities: an argument for a choice defeats another one if it is based on a computation that better uses all the available information. (shrink)

Most formalisms for representing common-sense knowledge allow incomplete and potentially inconsistent information. When strong negation is also allowed, contradictory conclusions can arise. A criterion for deciding between them is needed. The aim of this paper is to investigate an inherent and autonomous comparison criterion, based on specificity as defined in [POO 85, SIM 92]. In contrast to other approaches, we consider not only defeasible, but also strict knowledge. Our criterion is context-sensitive, i. e., preference among defeasible rules is determined dynamically (...) during the dialectical analysis.We show how specificity can be defined in terms of two different approaches: activation sets and derivation trees. This allows us to get a syntactic criterion that can be implemented in a computationally attractive way. The resulting definitions may be applied in general rulebased formalisms. We present theorems linking both characterizations. Finally we discuss other frameworks for defeasible reasoning in which preference handling is considered explicitly. (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)

This article proposes a formal analysis of a fundamental aspect of legal reasoning: dealing with normative conflicts. Firstly, examples are illustrated concerning the dynamics of legal systems, the application of rules and exceptions, and the semantic indeterminacy of legal sources. Then two approaches to cope with conflicting information are presented: the preferred theories of Brewka, and the belief change functions of Alchourrón, Gärdenfors, and Makinson. The relations between those approaches are closely examined, and some aspects of a model of reasoning (...) with normative conflicts are outlined. Since this model takes into account an ordering of the involved regulations, criteria to order legal norms are finally specified. (shrink)

It is often necessary and reasonable to justify preferences before reasoning from them. Moreover, justifying a preference ordering is reduced to justifying the criterion that produces the ordering. This paper builds on the well-known ASPIC+ formalism to develop a model that integrates justifying qualitative preferences with reasoning from the justified preferences. We first introduce a notion of preference criterion in order to model the way in which preferences are justified by an argumentation framework. We also adapt the notion of argumentation (...) theory to build a sequence of argumentation frameworks, in which an argumentation framework justifies preferences that are to underlie the next framework. That is, in our formalism, preferences become not only an input of an argumentation framework, but also an output of it. This kind of input-output process can be applied in the further steps of argumentation. We also explore some interesting properties of our formalism. (shrink)

In this paper we will analyse the issue of defeasibility in the law, taking into account research carried out in philosophy, artificial intelligence and legal theory. We will adopt a very general idea of legal defeasibility, in which we will include all different ways in which certain legal conclusions may need to be abandoned, though no mistake was made in deriving them. We will argue that defeasibility in the law involves three different aspects, which we will call inference‐based defeasibility, process‐based (...) defeasibility, and theory‐based defeasibility. Only the integration of these three perspectives allows us to provide a satisfactory account of the role of defeasibility in legal reasoning. (shrink)

This article investigates to what extent protocols for dynamicdisputes, i.e., disputes in which the information base can vary at differentstages, can be justified in terms of logics for defeasible argumentation. Firsta general framework is formulated for dialectical proof theories for suchlogics. Then this framework is adapted to serve as a framework for protocols fordynamic disputes, after which soundness and fairness properties are formulated for such protocols relative to dialectical proof theories. It then turns out that certaintypes of protocols that are (...) perfectly fine with a static information base, arenot sound or fair in a dynamic setting. Finally, a natural dynamic protocolis defined for which soundness and fairness can be established. (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)

John Pollock (1940?2009) was an influential American philosopher who made important contributions to various fields, including epistemology and cognitive science. In the last 25 years of his life, he also contributed to the computational study of defeasible reasoning and practical cognition in artificial intelligence. He developed one of the first formal systems for argumentation-based inference and he put many issues on the research agenda that are still relevant for the argumentation community today. This paper presents an appreciation of Pollock's work (...) on defeasible reasoning and its relevance for the computational study of argument. In our opinion, Pollock deserves to be remembered as one of the founding fathers of the field of computational argument, while, moreover, his work contains important lessons for current research in this field, reminding us of the richness of its object of study. (shrink)

Inspired by legal reasoning, this paper presents a formal framework for assessing conflicting arguments. Its use is illustrated with applications to realistic legal examples, and the potential for implementation is discussed. The framework has the form of a logical system for defeasible argumentation. Its language, which is of a logic-programming-like nature, has both weak and explicit negation, and 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 proof theory of the system 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. Despite this dialectical form, the system reflects a declarative, or relational approach to modelling legal argument. A basic assumption of this paper is that this approach complements two other lines of research in AI and Law, investigations of precedent-based reasoning and the development of procedural, or dialectical models of legal argument. (shrink)

The question addressed in this paper is how the degree of justification of a belief is determined. A conclusion may be supported by several different arguments, the arguments typically being defeasible, and there may also be arguments of varying strengths for defeaters for some of the supporting arguments. What is sought is a way of computing the “on sum” degree of justification of a conclusion in terms of the degrees of justification of all relevant premises and the strengths of all (...) relevant reasons. (shrink)

This paper presents a comprehensive study of argumentation frameworks with necessities (AFNs), a bipolar extension of Dung Abstract argumentation frameworks (AFs) where the support relation captures a positive interaction between arguments having the meaning of necessity: the acceptance of an argument may require the acceptance of other argument(s). The paper discusses new main acceptability semantics for AFNs and their characterization both by a direct approach and a labelling approach. It examines the relationship between AFNs and Dung AFs and shows the (...) gain provided by the former in terms of concision. Finally, the paper shows how to represent an AFN as a normal logic program (LP) and vice versa and in both cases establishes a one-to-one correspondence between extensions under the main acceptability semantics (except for semi-stable semantics where the correspondence is not completely full) of an AFN and particular cases of 3-valued stable models of normal LPs. (shrink)

We discuss five kinds of representations of rationales and provide a formal account of how they can alter disputation. The formal model of disputation is derived from recent work in argument. The five kinds of rationales are compilation rationales, which can be represented without assuming domain-knowledge (such as utilities) beyond that normally required for argument. The principal thesis is that such rationales can be analyzed in a framework of argument not too different from what AI already has. The result is (...) a formal understanding of rationales, a partial taxonomy, and a foundation for computer programs that represent and reason with rationales.The five kinds of rationales are as follows: (c)ompression and (s)pecialization, which yield rules, and (d)isputation, which yields a decision. These are modeled as potentially changing the focus of the dispute. Then there are (f)it, a rationale for rules, and (r)esolution, a rationale for decisions. These cannot be modeled as simply; they force disputation to a meta-level, at least temporarily. (shrink)

The first issue of _Artificial Intelligence and Law_ journal was published in 1992. This paper provides commentaries on landmark papers from the first decade of that journal. The topics discussed include reasoning with cases, argumentation, normative reasoning, dialogue, representing legal knowledge and neural networks.

Over the last decade, several extensions of Dung’s Abstract Argumentation Frameworks (AFs) have been introduced in the literature. Some of these extensions concern the nature of the attack relation, such as the consideration of recursive attacks, whereas others incorporate additional interactions, such as a support relation. Recently, the Attack–Support Argumentation Framework (ASAF) was proposed, which accounts for recursive attacks and supports, attacks to supports and supports to attacks, at any level, where the support relation is interpreted as necessity. Currently, to (...) determine the accepted elements of an ASAF (which may be arguments, attacks, and supports) it is required to translate such an ASAF into a Dung’s AF. In this work, we provide a formal characterization of acceptability semantics directly on the ASAF, without requiring such a translation. We prove that our characterization is sound since it satisfies different results from Dung’s argumentation theory; moreover, we formally show that the approach proposed here for addressing acceptability is equivalent to the preexisting one, in which the ASAF was translated into an AF. Also, we formalize the relationship between the ASAF and other frameworks on which it is inspired: the Argumentation Framework with Recursive Attacks (AFRA) and the Argumentation Framework with Necessities (AFN). (shrink)

We present a formal, mathematical model of argument structure and evaluation, taking seriously the procedural and dialogical aspects of argumentation. The model applies proof standards to determine the acceptability of statements on an issue-by-issue basis. The model uses different types of premises (ordinary premises, assumptions and exceptions) and information about the dialectical status of statements (stated, questioned, accepted or rejected) to allow the burden of proof to be allocated to the proponent or the respondent, as appropriate, for each premise separately. (...) Our approach allows the burden of proof for a premise to be assigned to a different party than the one who has the burden of proving the conclusion of the argument, and also to change the burden of proof or applicable proof standard as the dialogue progresses from stage to stage. Useful for modeling legal dialogues, the burden of production and burden of persuasion can be handled separately, with a different responsible party and applicable proof standard for each. Carneades enables critical questions of argumentation schemes to be modeled as additional premises, using premise types to capture the varying effect on the burden of proof of different kinds of questions. (shrink)

Argumentation represents a way of reasoning over a knowledge base containing possibly incomplete and/or inconsistent information, to obtain useful conclusions. As a reasoning mechanism, the way an argumentation reasoning engine reaches these conclusions resembles the cognitive process that humans follow to analyze their beliefs; thus, unlike other computationally reasoning systems, argumentation offers an intellectually friendly alternative to other defeasible reasoning systems. LogicProgrammingisacomputationalparadigmthathasproducedcompu- tationallyattractivesystemswithremarkablesuccessinmanyapplications. Merging ideas from both areas, Defeasible Logic Programming offers a computational reasoning system that uses an argumentation engine (...) to obtain answers from a knowledge base represented using a logic programming language extended with defeasible rules. This combination of ideas brings about a computationally effective system together with a human-like reasoning model facilitating its use in applications. (shrink)

Most formalisms for representing common-sense knowledge allow incomplete and potentially inconsistent information. When strong negation is also allowed, contradictory conclusions can arise. A criterion for deciding between them is needed. The aim of this paper is to investigate an inherent and autonomous comparison criterion, based on specificity as defined in [POO 85, SIM 92]. In contrast to other approaches, we consider not only defeasible, but also strict knowledge. Our criterion is context-sensitive, i. e., preference among defeasible rules is determined dynamically (...) during the dialectical analysis.We show how specificity can be defined in terms of two different approaches: activation sets and derivation trees. This allows us to get a syntactic criterion that can be implemented in a computationally attractive way. The resulting definitions may be applied in general rulebased formalisms. We present theorems linking both characterizations. Finally we discuss other frameworks for defeasible reasoning in which preference handling is considered explicitly. (shrink)

We propose a revision operator on a stratified belief base, i.e., a belief base that stores beliefs in different strata corresponding to the value an agent assigns to these beliefs. Furthermore, the operator will be defined as to perform the revision in such a way that information is never lost upon revision but stored in a stratum or layer containing information perceived as having a lower value. In this manner, if the revision of one layer leads to the rejection of (...) some information to maintain consistency, instead of being withdrawn it will be kept and introduced in a different layer with lower value. Throughout this development we will follow the principle of minimal change, being one of the important principles proposed in belief change theory, particularly emphasized in the AGM model. Regarding the reasoning part from the stratified belief base, the agent will obtain the inferences using an argumentative formalism. Thus, the argumentation framework will decide which information prevails when sentences of different layers are used for entailing conflicting beliefs. We will also illustrate how inferences are changed and how the status of arguments can be modified after a revision process. (shrink)

In this article we explore multiple change operators, i.e., operators in which the epistemic input is a set of sentences instead of a single sentence. We propose two types of change: prioritized change, in which the input set is fully accepted, and symmetric change, where both the epistemic state and the epistemic input are equally treated. In both kinds of operators we propose a set of postulates and we present different constructions: kernel changes and partial meet changes.

We present different constructions for nonprioritized belief revision, that is, belief changes in which the input sentences are not always accepted. First, we present the concept of explanation in a deductive way. Second, we define multiple revision operators with respect to sets of sentences (representing explanations), giving representation theorems. Finally, we relate the formulated operators with argumentative systems and default reasoning frameworks.

The problem of knowledge evolution has received considerable attention over the years. Mainly, the study of the dynamics of knowledge has been addressed in the area of Belief Revision, a field emerging as the convergence of the efforts in Philosophy, Logic, and more recently Computer Science, where research efforts usually involve “flat” knowledge bases where there is no additional information about the formulas stored in it. Even when this may be a good fit for particular applications, in many real-world scenarios (...) different information items may be attached to formulas. For instance, when the reliability of the source of the piece of information is attached to it as a measure of some quality (e.g., strength) of the piece of information itself, or when some characteristic informs us on the desirability of the item (e.g., the potential benefit that could be obtained from it). If this type of information is available, we can use it to guide how the belief base is to be modified when new information arrives. In this work, we present a novel approach to the contraction of knowledge bases where formulas have values attached that measure some quality linked to those formulas, exploiting it to define their desirability, and uses such desirability to define which formulas need to be removed to solve conflicts. In this context, we introduce a set of properties for contraction operators by extending classic approaches. We also show how the local treatment of minimal conflicts can induce some counter-intuitive contractions, and we present a way to avoid them by considering optimal resolutions of conflicts using the additional information encoded. We show how the proposed formalization captures any contraction that is optimal under a set of features. Finally, we present a refinement based on the identification of related minimal conflicts that performs contraction in optimal ways without looking into the entire knowledge base. The approach is based on the use of the accrual of beliefs where several formulas collaboratively use their respective values to prevail in the resolution of conflicts. (shrink)

We present two prudent semantics within Dung's theory of argumentation. They are based on two new notions of extension, referred to as p-extension and c-extension. Two arguments cannot belong to the same p-extension whenever one of them attacks indirectly the other one. Two arguments cannot belong to the same c-extension whenever one of them indirectly attacks a third argument while the other one indirectly defends the third. We argue that our semantics lead to a better handling of controversial arguments than (...) Dung's ones. We compare the prudent inference relations induced by our semantics w.r.t. cautiousness; we also compare them with the inference relations induced by Dung's semantics. (shrink)

. Artificial Intelligence (AI) has long dealt with the issue of finding a suitable formalization for commonsense reasoning. Defeasible argumentation has proven to be a successful approach in many respects, proving to be a confluence point for many alternative logical frameworks. Different formalisms have been developed, most of them sharing the common notions of argument and warrant. In defeasible argumentation, an argument is a tentative (defeasible) proof for reaching a conclusion. An argument is warranted when it ultimately prevails over other (...) conflicting arguments. In this context, defeasible consequence relationships for modelling argument and warrant as well as their logical properties have gained particular attention. This article analyzes two non-monotonic inference operators Carg and Cwar intended for modelling argument construction and dialectical analysis (warrant), respectively. As a basis for such analysis we will use the LDSar framework, a unifying approach to computational models of argument using Labelled Deductive Systems (LDS). In the context of this logical framework, we show how labels can be used to represent arguments as well as argument trees, facilitating the definition and study of non-monotonic inference operators, whose associated logical properties are studied and contrasted. We contend that this analysis provides useful comparison criteria that can be extended and applied to other argumentation frameworks. (shrink)