scholarly journals Closure and Consistency In Logic-Associated Argumentation

2014 ◽  
Vol 49 ◽  
pp. 79-109 ◽  
Author(s):  
P. M. Dung ◽  
P. M. Thang
Keyword(s):  
Logic Programming ◽  
The Self ◽  
Argumentation Framework ◽  
Natural Properties ◽  
Abstract Argumentation ◽  
Reasoning System ◽  
Consistency Property ◽  
Abstract Logics ◽  
Consistency Properties ◽  
Rule Out

Properties like logical closure and consistency are important properties in any logical reasoning system. Caminada and Amgoud showed that not every logic-based argument system satisfies these relevant properties. But under conditions like closure under contraposition or transposition of the monotonic part of the underlying logic, ASPIC-like systems satisfy these properties. In contrast, the logical closure and consistency properties are not well-understood for other well-known and widely applied systems like logic programming or assumption based argumentation. Though conditions like closure under contraposition or transposition seem intuitive in ASPIC-like systems, they rule out many sensible ASPIC-like systems that satisfy both properties of closure and consistency. We present a new condition referred to as the self-contradiction axiom that guarantees the consistency property in both ASPIC-like and assumption-based systems and is implied by both properties of closure under contraposition or transposition. We develop a logic-associated abstract argumentation framework, by associating abstract argumentation with abstract logics to represent the conclusions of arguments. We show that logic-associated abstract argumentation frameworks capture ASPIC-like systems (without preferences) and assumption-based argumentation. We present two simple and natural properties of compactness and cohesion in logic-associated abstract argumentation frameworks and show that they capture the logical closure and consistency properties. We demonstrate that in both assumption-based argumentation and ASPIC-like systems, cohesion follows naturally from the self-contradiction axiom. We further give a translation from ASPIC-like systems (without preferences) into equivalent assumption-based systems that keeps the self-contradiction axiom invariant.

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 On the Semantics of Abstract Argumentation Frameworks: A Logic Programming Approach

2020 ◽  
Vol 20 (5) ◽  
pp. 703-718
Author(s):  
Gianvincenzo Alfano ◽  
Sergio Greco ◽  
Francesco Parisi ◽  
Irina Trubitsyna
Keyword(s):  
Logic Programming ◽  
Logic Program ◽  
Programming Approach ◽  
Logic Programs ◽  
Argumentation Framework ◽  
Abstract Argumentation ◽  
Stable Models

AbstractRecently there has been an increasing interest in frameworks extending Dung’s abstract Argumentation Framework (AF). Popular extensions include bipolar AFs and AFs with recursive attacks and necessary supports. Although the relationships between AF semantics and Partial Stable Models (PSMs) of logic programs has been deeply investigated, this is not the case for more general frameworks extending AF.In this paper we explore the relationships between AF-based frameworks and PSMs. We show that every AF-based framework Δ can be translated into a logic program PΔ so that the extensions prescribed by different semantics of Δ coincide with subsets of the PSMs of PΔ. We provide a logic programming approach that characterizes, in an elegant and uniform way, the semantics of several AF-based frameworks. This result allows also to define the semantics for new AF-based frameworks, such as AFs with recursive attacks and recursive deductive supports.

Some model theory for game logics

1979 ◽  
Vol 44 (2) ◽  
pp. 147-152
Author(s):  
Judy Green
Keyword(s):  
Model Theory ◽  
Existence Theorems ◽  
Semantic Interpretation ◽  
Rule Based ◽  
Game Logic ◽  
Important Method ◽  
Consistency Property ◽  
Consistency Properties ◽  
Model Existence

Consistency properties and their model existence theorems have provided an important method of constructing models for fragments of L∞ω. In [E] Ellentuck extended this construction to Suslin logic. One of his extensions, the Borel consistency property, has its extra rule based not on the semantic interpretation of the extra symbols but rather on a theorem of Sierpinski about the classical operation . In this paper we extend that consistency property to the game logic LG and use it to show how one can extend results about and its countable fragments to LG and certain of its countable fragments. The particular formation of LG which we use will allow in the game quantifier infinite alternation of countable conjunctions and disjunctions as well as infinite alternation of quantifiers. In this way LG can be viewed as an extension of Suslin logic.

scholarly journals The Subject of Critique: Ricoeur in Dialogue with Feminist Philosophers

2013 ◽  
Vol 4 (1) ◽  
pp. 21-39
Author(s):  
Annemie Halsema
Keyword(s):  
Feminist Theory ◽  
Thought Experiments ◽  
The Self ◽  
Major Point ◽  
The Subject ◽  
Rule Out

This paper aims to show the relevance of Ricœur’s notion of the self for postmodern feminist theory, but also to critically assess it. By bringing Ricœur’s “self” into dialogue with Braidotti’s, Irigaray’s and Butler’s conceptions of the subject, it shows that it is close to the feminist self in that it is articulated into language, is embodied and not fully conscious of itself. In the course of the argument, the major point of divergence also comes to light, namely, that the former considers discourse to be a laboratory for thought experiments, while the latter consider discourse to be normative, restrictive and exclusive. In the second part, the possibility of critique and change are further developed. Ricœur does not rule out critique, rather interpretation includes distanciation and critique. Finally, his notion of productive imagination explains how new identifications become possible. 

Hegel's System of Needs: The Elementary Relations of Economic Justice

1998 ◽  
Vol 19 (1-2) ◽  
pp. 51-72
Author(s):  
David Merrill
Keyword(s):  
Civil Society ◽  
Economic Justice ◽  
The Self ◽  
Self Determination ◽  
Social Character ◽  
Natural Necessity ◽  
Philosophy Of Right ◽  
Characteristic Features ◽  
Rule Out

The Philosophy of Right is not usually taken to contain a prescriptive ethics. Yet to establish as much regarding the elementary relations of the economy is the task of this essay. The project is cast into three parts. It begins with Hegel's account in the ‘Introduction’ of the free self prior to the exposition of the modes of just conduct or philosophy of right proper. It is an account of freedom not yet realized — without any particular content. Yet, the point is established that the philosophy of justice will be based on a twofold notion of self-determination. Most of the ‘Introduction’ concerns the argument that freedom or valid conduct has to do with pure self-determination, the self determining itself. The claim is also made that philosophy establishes its own legitimacy through its conceptual self-determination. Part two deals with the question of how freedom can be realized in civil society where the individual's governing orientation is particularity. The characteristic features of civil society do not encourage the expectation that freedom can be realized there. One, particularity itself appears to be rooted in a natural necessity which seems to preclude any possibility of freedom. Two, the inherently social character of civil society seems to rule out the exercise of a freedom that is about the self's relation to itself in self-determination. Three, the pursuit of particularity characteristic of civil society seems inherently antisocial and thus not a suitable mode of conduct for ethics. However, the argument will be made that the theory can conceive of the relations of particularity in a way that makes the free self inherently social and particularity both social and free from natural determinations.

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.

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