A logic of defeasible argumentation: Constructing arguments in justification logic

2020 ◽  
pp. 1-45
Author(s):  
Stipe Pandžić
Keyword(s):  
Operational Semantics ◽  
Formal System ◽  
Default Logic ◽  
Epistemic Reasons ◽  
Justification Logic ◽  
Argumentation Framework ◽  
Abstract Argumentation ◽  
Defeasible Argumentation ◽  
Key Features ◽  
Special Case

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 (1) Dung’s frameworks can be obtained from justification logic-based theories by focusing on a single aspect of attacks among justification logic arguments and (2) 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.

scholarly journals Revisiting the Foundations of Abstract Argumentation – Semantics Based on Weak Admissibility and Weak Defense

2020 ◽  
Vol 34 (03) ◽  
pp. 2742-2749
Author(s):  
Ringo Baumann ◽  
Gerhard Brewka ◽  
Markus Ulbricht
Keyword(s):  
Classical Case ◽  
Research Area ◽  
Major Research ◽  
Abstract Argumentation ◽  
New Concepts ◽  
Key Concepts ◽  
Problematic Issue ◽  
Rigorous Study ◽  
Grounded Semantics ◽  
Special Case

In his seminal 1995 paper, Dung paved the way for abstract argumentation, a by now major research area in knowledge representation. He pointed out that there is a problematic issue with self-defeating arguments underlying all traditional semantics. A self-defeat occurs if an argument attacks itself either directly or indirectly via an odd attack loop, unless the loop is broken up by some argument attacking the loop from outside. Motivated by the fact that such arguments represent self-contradictory or paradoxical arguments, he asked for reasonable semantics which overcome the problem that such arguments may indeed invalidate any argument they attack. This paper tackles this problem from scratch. More precisely, instead of continuing to use previous concepts defined by Dung we provide new foundations for abstract argumentation, so-called weak admissibility and weak defense. After showing that these key concepts are compatible as in the classical case we introduce new versions of the classical Dung-style semantics including complete, preferred and grounded semantics. We provide a rigorous study of these new concepts including interrelationships as well as the relations to their Dung-style counterparts. The newly introduced semantics overcome the issue with self-defeating arguments, and they are semantically insensitive to syntactic deletions of self-attacking arguments, a special case of self-defeat.

Certain predicates defined by induction schemata

1953 ◽  
Vol 18 (1) ◽  
pp. 49-59 ◽  
Author(s):  
Hao Wang
Keyword(s):  
Number Theory ◽  
Set Theory ◽  
Formal System ◽  
General Notion ◽  
Constant Number ◽  
Natural Numbers ◽  
System L ◽  
Truth Definition ◽  
Consistency Proofs ◽  
Special Case

It is known that we can introduce in number theory (for example, the system Z of Hilbert-Bernays) by induction schemata certain predicates of natural numbers which cannot be expressed explicitly within the framework of number theory. The question arises how we can define these predicates in some richer system, without employing induction schemata. In this paper a general notion of definability by induction (relative to number theory), which seems to apply to all the known predicates of this kind, is introduced; and it is proved that in a system L1 which forms an extension of number theory all predicates which are definable by induction (hereafter to be abbreviated d.i.) according to the definition are explicitly expressible.In order to define such predicates and prove theorems answering to their induction schemata, we have to allow certain impredicative classes in L1. However, if we want merely to prove that for each constant number the special case of the induction schema for a predicate d.i. is provable, we do not have to assume the existence of impredicative classes. A certain weaker system L2, in which only predicative classes of natural numbers are allowed, is sufficient for the purpose. It is noted that a truth definition for number theory can be obtained in L2. Consistency proofs for number theory do not seem to be formalizable in L2, although they can, it is observed, be formalized in L1.In general, given any ordinary formal system (say Zermelo set theory), it is possible to define by induction schemata, in the same manner as in number theory, certain predicates which are not explicitly definable in the system. Here again, by extending the system in an analogous fashion, these predicates become expressible in the resulting system. The crucial predicate instrumental to obtaining a truth definition for a given system is taken as an example.

scholarly journals Paracoherent Answer Set Semantics meets Argumentation Frameworks

2019 ◽  
Vol 19 (5-6) ◽  
pp. 688-704
Author(s):  
GIOVANNI AMENDOLA ◽  
FRANCESCO RICCA
Keyword(s):  
Logic Programming ◽  
Logic Program ◽  
Great Success ◽  
Argumentation Framework ◽  
Computational Costs ◽  
Abstract Argumentation ◽  
Answer Set Semantics ◽  
Answer Sets ◽  
Answer Set

AbstractIn the last years, abstract argumentation has met with great success in AI, since it has served to capture several non-monotonic logics for AI. Relations between argumentation framework (AF) semantics and logic programming ones are investigating more and more. In particular, great attention has been given to the well-known stable extensions of an AF, that are closely related to the answer sets of a logic program. However, if a framework admits a small incoherent part, no stable extension can be provided. To overcome this shortcoming, two semantics generalizing stable extensions have been studied, namely semi-stable and stage. In this paper, we show that another perspective is possible on incoherent AFs, called paracoherent extensions, as they have a counterpart in paracoherent answer set semantics. We compare this perspective with semi-stable and stage semantics, by showing that computational costs remain unchanged, and moreover an interesting symmetric behaviour is maintained.

scholarly journals Reasoning with Inconsistent Possibilistic Ontologies by Applying Argument Accrual

2017 ◽  
Vol 17 (02) ◽  
pp. e16
Author(s):  
Sergio Alejandro Gómez
Keyword(s):  
Logic Programming ◽  
Description Logic ◽  
Logic Programs ◽  
Argumentation Framework ◽  
Abstract Argumentation ◽  
Possibilistic Logic ◽  
Grounded Semantics

We present an approach for performing instance checking in possibilistic description logic programming ontologies by accruing arguments that support the membership of individuals to concepts. Ontologies are interpreted as possibilistic logic programs where accruals of arguments as regarded as vertexes in an abstract argumentation framework. A suitable attack relation between accruals is defined. We present a reasoning framework with a case study and a Java-based implementation for enacting the proposed approach that is capable of reasoning under Dung’s grounded semantics.

scholarly journals A Fully Abstract Presheaf Semantics of SCCS with Finite Delay

1999 ◽  
Vol 6 (28) ◽  
Author(s):  
Thomas Troels Hildebrandt
Keyword(s):  
Operational Semantics ◽  
Denotational Semantics ◽  
Transition Systems ◽  
Finite Delay ◽  
Open Map ◽  
Special Case

We present a presheaf model for the observation of infinite as well<br />as finite computations. We apply it to give a denotational semantics of<br />SCCS with finite delay, in which the meanings of recursion are given by<br />final coalgebras and meanings of finite delay by initial algebras of the<br />process equations for delay. This can be viewed as a first step in representing<br />fairness in presheaf semantics. We give a concrete representation<br />of the presheaf model as a category of generalised synchronisation<br />trees and show that it is coreflective in a category of generalised transition<br />systems, which are a special case of the general transition systems<br />of Hennessy and Stirling. The open map bisimulation is shown to coincide<br />with the extended bisimulation of Hennessy and Stirling. Finally<br />we formulate Milners operational semantics of SCCS with finite delay<br />in terms of generalised transition systems and prove that the presheaf<br />semantics is fully abstract with respect to extended bisimulation.

scholarly journals Defining the Semantics of Abstract Argumentation Frameworks through Logic Programs and Partial Stable Models (Extended Abstract)

2021 ◽  
Author(s):  
Gianvincenzo Alfano ◽  
Sergio Greco ◽  
Francesco Parisi ◽  
Irina Trubitsyna
Keyword(s):  
Logic Program ◽  
Logic Programs ◽  
Argumentation Framework ◽  
Abstract Argumentation ◽  
Stable Models

Extensions of Dung’s Argumentation Framework (AF) include the class of Recursive Bipolar AFs (Rec-BAFs), i.e. AFs with recursive attacks and supports. We show that a Rec-BAF \Delta can be translated into a logic program P_\Delta so that the extensions of \Delta under different semantics coincide with subsets of the partial stable models of P_\Delta.

scholarly journals Predictive models and abstract argumentation: the case of high-complexity semantics

2019 ◽  
Vol 34 ◽  
Author(s):  
Mauro Vallati ◽  
Federico Cerutti ◽  
Massimiliano Giacomin
Keyword(s):  
Predictive Models ◽  
Problem Instance ◽  
Sense Making ◽  
High Complexity ◽  
Algorithm Selection ◽  
Argumentation Framework ◽  
Abstract Argumentation ◽  
Complete Knowledge ◽  
Enumeration Problem ◽  
Human Sense

Abstract In this paper, we describe how predictive models can be positively exploited in abstract argumentation. In particular, we present two main sets of results. On one side, we show that predictive models are effective for performing algorithm selection in order to determine which approach is better to enumerate the preferred extensions of a given argumentation framework. On the other side, we show that predictive models predict significant aspects of the solution to the preferred extensions enumeration problem. By exploiting an extensive set of argumentation framework features—that is, values that summarize a potentially important property of a framework—the proposed approach is able to provide an accurate prediction about which algorithm would be faster on a given problem instance, as well as of the structure of the solution, where the complete knowledge of such structure would require a computationally hard problem to be solved. Improving the ability of existing argumentation-based systems to support human sense-making and decision processes is just one of the possible exploitations of such knowledge obtained in an inexpensive way.

Independence and D-separation in Abstract Argumentation

2020 ◽  
Author(s):  
Tjitze Rienstra ◽  
Matthias Thimm ◽  
Kristian Kersting ◽  
Xiaoting Shao
Keyword(s):  
Markov Property ◽  
Argumentation Framework ◽  
Separation Criterion ◽  
Abstract Argumentation ◽  
The Status ◽  
Definition Of ◽  
Semantic Definition

We investigate the notion of independence in abstract argumentation, i.e., the question of whether the evaluation of one set of arguments is independent of the evaluation of another set of arguments, given that we already know the status of a third set of arguments. We provide a semantic definition of this notion and develop a method to discover independencies based on transforming an argumentation framework into a DAG on which we then apply the well-known d-separation criterion. We also introduce the SCC Markov property for argumentation semantics, which generalises the Markov property from the classical acyclic case and guarantees the soundness of our approach.

Sign in / Sign up

Export Citation Format

Share Document