Cases or examples can be often explained by the interplay of arguments in favour or against their outcomes. This paper addresses the problem of finding explanations for a collection of cases where an explanation is a labelled argumentation graph consistent with the cases, and a case is represented as a statement labelling. The focus is on semi-abstract argumentation graphs specifying attack and subargument relations between arguments, along with particular complete argument labellings taken from probabilistic argumentation where arguments can be excluded. (...) The framework and computational considerations lead to an iterated local iterative deepening depth-first search to collect ‘interesting’ semi-abstract argumentation graphs consistent with a collection of statement labellings. Finally, the framework is illustrated and evaluated with a proof-of-concept implementation. (shrink)

In the 1980s, Pollock’s work on default reasons started the quest in the AI community for a formal system of defeasible argumentation. The main goal of this paper is to provide a logic of structured defeasible arguments using the language of justification logic. In this logic, we introduce defeasible justification assertions of the type t : F that read as “t is a defeasible reason that justifies F”. Such formulas are then interpreted as arguments and their acceptance semantics is given (...) in analogy to Dung’s abstract argumentation framework semantics. We show that a large subclass of Dung’s frameworks that we call “warranted” frameworks is a special case of our logic in the sense that Dung’s frameworks can be obtained from justification logic-based theories by focusing on a single aspect of attacks among justification logic arguments and Dung’s warranted frameworks always have multiple justification logic instantiations called “realizations”. We first define a new justification logic that relies on operational semantics for default logic. One of the key features that is absent in standard justification logics is the possibility to weigh different epistemic reasons or pieces of evidence that might conflict with one another. To amend this, we develop a semantics for “defeaters”: conflicting reasons forming a basis to doubt the original conclusion or to believe an opposite statement. This enables us to formalize non-monotonic justifications that prompt extension revision already for normal default theories. Then we present our logic as a system for abstract argumentation with structured arguments. The format of conflicting reasons overlaps with the idea of attacks between arguments to the extent that it is possible to define all the standard notions of argumentation framework extensions. Using the definitions of extensions, we establish formal correspondence between Dung’s original argumentation semantics and our operational semantics for default theories. One of the results shows that the notorious attack cycles from abstract argumentation cannot always be realized as justification logic default theories. (shrink)

There are many benefits of using argumentation-based techniques in multi-agent systems, as clearly shown in the literature. Such benefits come not only from the expressiveness that argumentation-based techniques bring to agent communication but also from the reasoning and decision-making capabilities under conditions of conflicting and uncertain information that argumentation enables for autonomous agents. When developing multi-agent applications in which argumentation will be used to improve agent communication and reasoning, argumentation schemes are useful in addressing the requirements of the application domain (...) in regards to argumentation. In this work, we propose an argumentation framework that takes into account the particular structure of argumentation schemes at its core. This paper formally defines such a framework and experimentally evaluates its implementation for both argumentation-based reasoning and dialogues. (shrink)

The connection between logic programming and formal argumentation has been studied starting from the landmark 1995 paper of Dung. Subsequent work has identified a standard translation from logic programs to argumentation frameworks, under which pairwise correspondences hold between various logic programming semantics and various formal argumentation semantics. This includes the correspondence between 3-valued stable and complete semantics, between well-founded and grounded semantics and between 2-valued stable and stable semantics. In the current paper, we show that the existing translation is able (...) to yield the additional correspondence between ideal semantics for logic programming and ideal semantics for formal argumentation. We also show that correspondence does not hold between eager semantics for logic programming and eager semantics for formal argumentation, at least when translating from logic programming to formal argumentation. Overall, the current work should be seen as completing the analysis of correspondences between mainstream admissibility-based argumentation semantics and their logic programming counterparts. (shrink)

This paper explores the relationship between informal reasoning, creativity in mathematics, and problem solving. It underscores the importance of environments that promote interaction, hypothesis generation, examination, refutation, derivation of new solutions, drawing conclusions, and reasoning with others, as key factors in enhancing mathematical creativity. Drawing on argumentation logic, the paper proposes a novel approach to uncover specific characteristics in the development of formalized proving using “proof-events.” Argumentation logic can offer reasoning mechanisms that facilitate these environments. This paper proposes how argumentation (...) can be implemented to discover certain characteristics in the development of formalized proving with “proof-events”. The concept of a proof-event was introduced by Goguen who described mathematical proof as a multi-agent social event involving not only “classical” formal proofs, but also other informal proving actions such as deficient or alleged proofs. Argumentation is an integral component of the discovery process for a mathematical proof since a proof necessitates a dialogue between provers and interpreters to clarify and resolve gaps or assumptions. By formalizing proof-events through argumentation, this paper demonstrates how informal reasoning and conflicts arising during the proving process can be effectively simulated. The paper presents an extended version of the proof-events calculus, rooted in argumentation theories, and highlights the intricate relationships among proof, human reasoning, cognitive processes, creativity, and mathematical arguments. (shrink)

Structured argumentation systems, and their implementation, represent an important research subject in the area of Knowledge Representation and Reasoning. Structured argumentation advances over abstract argumentation frameworks by providing the internal construction of the arguments that are usually defined by a set of (strict and defeasible) rules. By considering the structure of arguments, it becomes possible to analyze reasons for and against a conclusion, and the warrant status of such a claim in the context of a knowledge base represents the main (...) output of a dialectical process. Computing such statuses is a costly process, and any update to the knowledge base could potentially have a huge impact if done naively. In this work, we investigate the case of updates consisting of both additions and removals of pieces of knowledge in the Defeasible Logic Programming (DeLP) framework, first analyzing the complexity of the problem and then identifying conditions under which we can avoid unnecessary computations—central to this is the development of structures (e.g. graphs) to keep track of which results can potentially be affected by a given update. We introduce a technique for the incremental computation of the warrant statuses of conclusions in DeLP knowledge bases that evolve due to the application of (sets of) updates. We present the results of a thorough experimental evaluation showing that our incremental approach yields significantly faster running times in practice, as well as overall fewer recomputations, even in the case of sets of updates performed simultaneously. (shrink)

This paper develops a logical theory that unifies all three standard types of argumentative attack in AI, namely rebutting, undercutting and undermining attacks. We build on default justification logic that already represents undercutting and rebutting attacks, and we add undermining attacks. Intuitively, undermining does not target default inference, as undercutting, or default conclusion, as rebutting, but rather attacks an argument’s premise as a starting point for default reasoning. In default justification logic, reasoning starts from a set of premises, which is (...) then extended by conclusions that hold by default. We argue that modeling undermining defeaters in the view of default theories requires changing the set of premises upon receiving new information. To model changes to premises, we give a dynamic aspect to default justification logic by using the techniques from the logic of belief revision. More specifically, undermining is modeled with belief revision operations that include contracting a set of premises, that is, removing some information from it. The novel combination of default reasoning and belief revision in justification logic enriches both approaches to reasoning under uncertainty. By the end of the paper, we show some important aspects of defeasible argumentation in which our logic compares favorably to structured argumentation frameworks. (shrink)

This text is expository. We explain Gödel’s ‘Master Argument’ for incompleteness as distinguished from the 'official' proof of his 1931 paper, highlight its attractions and limitations, and explain how some of the limitations may be transcended by putting it in a more abstract form that makes no reference to truth.