Propositional discourse logic

Dyrkolbotn, Sjur K.; Walicki, Michał

doi:10.1007/s11229-013-0297-x

Cited by 21 publications

(23 citation statements)

References 28 publications

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“…Given a BAF A = (A, →, ⇒), this enables to define the neutrality function n ns A : P(A) −→ P(A) as: n ns A (X) = {x ∈ A : NOT X →⇒ * x} and the defense function d ns A : P(A) −→ P(A) as: d ns A (X) = {x ∈ A : ∀y ∈ A : IF y →⇒ * x THEN X →⇒ * y} This approach has the advantage of anchoring the definitions of the solution concepts to those provided by [?]. 11 For example, define…”

Section: Bipolar Argumentation Frameworkmentioning

confidence: 99%

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Bipolar Argumentation Frameworks, Modal Logic and Semantic Paradoxes

Proietti

Grossi

Smets

et al. 2019

Logic, Rationality, and Interaction

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Bipolar Argumentation Frameworks (BAF) are a natural extension of Dung's Argumentation Frameworks (AF) where a relation of support between arguments is added to the standard attack relation. Despite their interest, BAF present several difficulties and their semantics are quite complex. This paper provides a definition of semantic concepts for BAF in terms of fixpoints of the functions of neutrality and defense, thus preserving most of the fundamental properties of Dung's AF. From this angle it becomes easy to show that propositional dynamic logic provides an adequate language to talk about BAF. Finally, we illustrate how this framework allows to encode the structure of the referential discourse involved in semantic paradoxes such as the Liar. It turns out that such paradoxes can be seen as BAF without a stable extension. A further notion is that of evidential support [?] that we will not deal with here. 6 Carlo Proietti gratefully acknowledges funding received from the European Commission (Marie Skłodowska-Curie Individual Fellowship 2016, 748421) for his research. The authors would like to thank the anonymous reviewers of LORI'19 for many helpful suggestions. 4 Indeed, the only support available in standard AF is the "defense" relation: argument a supports argument b by attacking one of its attackers. This is too restrictive in most real-life debates, where arguments providing direct support are commonly used. 5 We limit ourselves to binary necessary support. Indeed this notion of support is often introduced as a more general relation between a set of arguments and an argument [?,?]. 6 Evidential support can be seen as a special kind of necessary support where an argument cannot be accepted unless it is ultimately supported by "evidence", the latter being a special

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Section: Bipolar Argumentation Frameworkmentioning

confidence: 99%

“…This is because both relations →⇒ * and (⇒ −1 ) * → are contained in relation (⇒ −1 ) * →⇒ * 11. In an analogous way we could assume extended or n+-attacks as our primitive notion and define the neutrality and defense function accordingly.…”

mentioning

confidence: 99%

Bipolar Argumentation Frameworks, Modal Logic and Semantic Paradoxes

Proietti

Grossi

Smets

et al. 2019

Logic, Rationality, and Interaction

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“…The authors make use of logical tools, relying both on a truth-functional three-valued view of argumentation [3,34], and on modal logic [40,41]. They focus "on the stepwise, iterative development of a common framework, and on the logical analysis of the different ways in which such a [deliberative] process may unfold, by way of a logical treatment of the modalities that arise from quantifying over the space of possible deliberative futures".…”

Section: Dynamic Argument Aggregationmentioning

confidence: 99%

Collective argumentation: A survey of aggregation issues around argumentation frameworks

Bodanza

Tohmé

Auday

2017

AAC

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Abstract. Dung's argumentation frameworks have been applied for over twenty years to the analysis of argument justification. This representation focuses on arguments and the attacks among them, abstracting away from other features like the internal structure of arguments, the nature of utterers, the specifics of the attack relation, etc. The model is highly attractive because it reduces most of the complexities involved in argumentation processes. It can be applied to different settings, like the argument evaluation of an individual agent or the case of dialectic disputes between two agents (pro and con), or even in multi-agent collective argumentation. The latter case involves agents with possibly different arguments and/or opinions on how to evaluate them, leading to the possibility of considering multiple sets of arguments and attack relations. Two basic questions can be asked here, namely 'what to aggregate' and 'how to aggregate'. The former concerns what kinds of entities do the agents intend to choose (arguments, attacks, assessments, etc.), while the second one focuses on which aggregation mechanisms yield rational choices (voting on arguments, merging procedures to obtain a common argumentation framework, deliberation processes, etc.). In particular, the question about the rationality of a collective argument choice relates this topic to Social Choice and Judgment Aggregation theories, while its associated strategic issues relate it to Game Theory. The research efforts on the disparate problems elicited by collective argumentation have generated a considerable corpus of literature that deserves an orderly evaluation. This survey is intended as a contribution to that end.

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“…The three-valued representation facilitates elegant definitions of various argumentation semantics, specifying sets of assignments rather than extensions. In this way, it also becomes natural to reason about AFs using three-valued logic, an idea that has been explored in some recent work Dyrkolbotn and Walicki (2014), Arieli andCaminada (2013), andDyrkolbotn (2013). This will be exploited in the coming sections, as we will rely on three-valued Łukasiewicz logic when we evaluate complex formulas over given AFs.…”

Section: Argumentation Framework Agents and Semantic Viewsmentioning

confidence: 99%

“…6 The theory of argumentation frameworks has been influential in the context of artificial intelligence (Rahwan and Simari 2009). It is capable of capturing many different semantic notions, including semantics for multi-valued and non-monotonic logics, logic programs and games (Dung 1995;Dyrkolbotn and Walicki 2014). The work of Brewka et al (2011), on the other hand, shows how argumentation frameworks can be used to provide a faithful (and computationally efficient) representation also of semantics that are formulated with respect to the more fine-grained formalism of abstract dialectical frameworks (Brewka and Gordon 2010).…”

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confidence: 99%

Arguably Argumentative: A Formal Approach to the Argumentative Theory of Reason

Dyrkolbotn

Pedersen

2016

Fundamental Issues of Artificial Intelligence

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We propose a formal approach to the argumentative theory of reason, combining argumentation theory and modal logic in a novel way. We show that the resulting framework can be used to model important mechanisms identified by the theory, including how confirmation bias and other problematic modes of reasoning may in fact serve an important argumentative purpose that can give rise to classically sound conclusions through the process of social deliberation. We go on to suggest that the argumentative theory is based on an understanding of intelligent reasoning and rationality that sees these notions as irreducibly social, and that the argumentative theory itself provides a possible starting point in the search for new theoretical foundations based on this understanding. Moreover, we suggest that formal logic can aid in the investigation of foundational issues, and we sketch the development of an axiomatic approach to the study of rational deliberation.

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Propositional discourse logic

Cited by 21 publications

References 28 publications

Bipolar Argumentation Frameworks, Modal Logic and Semantic Paradoxes

Bipolar Argumentation Frameworks, Modal Logic and Semantic Paradoxes

Collective argumentation: A survey of aggregation issues around argumentation frameworks

Arguably Argumentative: A Formal Approach to the Argumentative Theory of Reason

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