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See detailOn the Entailment Problem for a Logic of Typicality
Booth, Richard UL; Casini, Giovanni UL; Meyer, Thomas et al

in Yang, Qiang; Wooldridge, Michael (Eds.) Proceedings of the TwentyFourth International Joint Conference on Artificial Intelligence. Buenos Aires, Argentina, 25–31 July 2015 (2015)

Propositional Typicality Logic (PTL) is a recently proposed logic, obtained by enriching classical propositional logic with a typicality operator. In spite of the non-monotonic features introduced by the ... [more ▼]

Propositional Typicality Logic (PTL) is a recently proposed logic, obtained by enriching classical propositional logic with a typicality operator. In spite of the non-monotonic features introduced by the semantics adopted for the typicality operator, the obvious Tarskian definition of entailment for PTL remains monotonic and is therefore not appropriate. We investigate different (semantic) versions of entailment for PTL, based on the notion of Rational Closure as defined by Lehmann and Magidor for KLM-style conditionals, and constructed using minimality. Our first important result is an impossibility theorem showing that a set of proposed postulates that at first all seem appropriate for a notion of entailment with regard to typicality cannot be satisfied simultaneously. Closer inspection reveals that this result is best interpreted as an argument for advocating the development of more than one type of PTL entailment. In the spirit of this interpretation, we define two primary forms of entailment for PTL and discuss their advantages and disadvantages. [less ▲]

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See detailTowards Dialogue Games for the Down-Admissible and Up-Complete Procedures
Caminada, Martin; Booth, Richard UL

E-print/Working paper (2014)

Recently, two operators - the down-admissible and up-complete operators - have been proposed, in the context of aggregating argument labellings, for repairing a given initial labelling so that it becomes ... [more ▼]

Recently, two operators - the down-admissible and up-complete operators - have been proposed, in the context of aggregating argument labellings, for repairing a given initial labelling so that it becomes rational, in the sense that it respects the attack relation between the arguments. The purpose of this research note is to give some initial thoughts on defining dialogue games for each of them, as well as for their combination. [less ▲]

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See detailA logical theory about dynamics in abstract argumentation
Booth, Richard UL; Kaci, Souhila; Rienstra, Tjitze UL et al

Scientific Conference (2013)

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See detailA logical theory about dynamics in abstract argumentation
Booth, Richard UL; Kaci, Souhila; Rienstra, Tjitze UL et al

Scientific Conference (2013)

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See detailA logical theory about dynamics in abstract argumentation
Booth, Richard UL; Kaci, Souhila; Rienstra, Tjitze UL et al

in Scalable Uncertainty Management - 7th International Conference, SUM 2013 (2013)

We address dynamics in abstract argumentation using a logical theory where an agent’s belief state consists of an argumentation framework (AF, for short) and a constraint that encodes the outcome the ... [more ▼]

We address dynamics in abstract argumentation using a logical theory where an agent’s belief state consists of an argumentation framework (AF, for short) and a constraint that encodes the outcome the agent believes the AF should have. Dynamics enters in two ways: (1) the constraint is strengthened upon learning that the AF should have a certain outcome and (2) the AF is expanded upon learning about new arguments/attacks. A problem faced in this setting is that a constraint may be inconsistent with the AF’s outcome. We discuss two ways to address this problem: First, it is still possible to form consistent fallback beliefs, i.e., beliefs that are most plausible given the agent’s AF and constraint. Second, we show that it is always possible to find AF expansions to restore consistency. Our work combines various individual approaches in the literature on argumentation dynamics in a general setting. [less ▲]

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See detailProperty-based preferences in abstract argumentation
Booth, Richard UL; Kaci, Souhila; Rienstra, Tjitze UL

in Algorithmic Decision Theory - Third International Conference, ADT 2013 (2013)

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See detailA propositional typicality logic for extending rational consequence
Booth, Richard UL; Meyer, Thomas; Varzinczak, Ivan

in Trends in Belief Revision and Argumentation Dynamics (2013)

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See detailMonotonic and non-monotonic inference for abstract argumentation
Booth, Richard UL; Kaci, Souhila; Rienstra, Tjitze UL et al

in Proceedings of the Twenty-Sixth International Florida Artificial Intelligence Research Society Conference, FLAIRS 2013 (2013)

We present a new approach to reasoning about the outcome of an argumentation framework, where an agent’s reasoning with a framework and semantics is represented by an inference relation defined over a ... [more ▼]

We present a new approach to reasoning about the outcome of an argumentation framework, where an agent’s reasoning with a framework and semantics is represented by an inference relation defined over a logical labeling language. We first study a monotonic type of inference which is, in a sense, more general than an acceptance function, but equally expressive. In order to overcome the limitations of this expressiveness, we study a non-monotonic type of inference which allows counterfactual inferences. We precisely characterize the classes of frameworks distinguishable by the non-monotonic inference relation for the admissible semantics. [less ▲]

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See detailCredibility-limited revision operators in propositional logic
Booth, Richard UL; Fermé, Eduardo; Konieczny, Sébastien et al

Scientific Conference (2012)

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See detailConditional acceptance functions
Booth, Richard UL; Kaci, Souhila; Rienstra, Tjitze UL et al

in 4th International Conference on Computational Models of Argument (COMMA 2012) (2012)

Dung-style abstract argumentation theory centers on argumentation frameworks and acceptance functions. The latter take as input a framework and return sets of labelings. This methodology assumes full ... [more ▼]

Dung-style abstract argumentation theory centers on argumentation frameworks and acceptance functions. The latter take as input a framework and return sets of labelings. This methodology assumes full awareness of the arguments relevant to the evaluation. There are two reasons why this is not satisfactory. Firstly, full awareness is, in general, not a realistic assumption. Second, frameworks have explanatory power, which allows us to reason abductively or counterfactually, but this is lost under the usual semantics. To recover this aspect, we generalize conventional acceptance, and we present the concept of a conditional acceptance function. [less ▲]

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See detailPTL: A propositional typicality logic
Booth, Richard UL; Meyer, Thomas; Vazinczak, Ivan

in 13th Conference on Logics in Artificial Intelligence (JELIA 2012) (2012)

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See detailA general family of preferential belief removal operators
Booth, Richard UL; Meyer, Thomas; Sombattheera, Chattrakul

in Journal of Philosophical Logic (2012), 41(4), 711-733

Most belief change operators in the AGM tradition assume an underlying plausibility ordering over the possible worlds which is transitive and complete. A unifying structure for these operators, based on ... [more ▼]

Most belief change operators in the AGM tradition assume an underlying plausibility ordering over the possible worlds which is transitive and complete. A unifying structure for these operators, based on supplementing the plausibility ordering with a second, guiding, relation over the worlds was presented in Booth et al. (Artif Intell 174:1339–1368, 2010). However it is not always reasonable to assume completeness of the underlying ordering. In this paper we generalise the structure of Booth et al. (Artif Intell 174:1339–1368, 2010) to allow incomparabilities between worlds. We axiomatise the resulting class of belief removal functions, and show that it includes an important family of removal functions based on finite prioritised belief bases. [less ▲]

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See detailQuantifying disagreement in argument-based reasoning
Booth, Richard UL; Caminada, Martin UL; Podlaszewski, Mikołaj UL et al

in 11th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2012) (2012)

An argumentation framework can be seen as expressing, in an abstract way, the conflicting information of an underlying logical knowledge base. This conflicting information often allows for the presence of ... [more ▼]

An argumentation framework can be seen as expressing, in an abstract way, the conflicting information of an underlying logical knowledge base. This conflicting information often allows for the presence of more than one possible reasonable position (extension/labelling) which one can take. A relevant question, therefore, is how much these positions differ from each other. In the current paper, we will examine the issue of how to define meaningful measures of distance between the (complete) labellings of a given argumentation framework. We provide concrete distance measures based on argument-wise label difference, as well as based on the notion of critical sets, and examine their properties. [less ▲]

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See detailCredibility-limited revision operators in propositional logic
Booth, Richard UL; Fermé, Eduardo; Konieczny, Sébastien et al

in 13th International Conference on Principles of Knowledge Representation and Reasoning (KR 2012) (2012)

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See detailHow to revise a total preorder
Booth, Richard UL; Meyer, Thomas

in Journal of Philosophical Logic (2011), 40

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See detailLearning conditionally lexicographic preference relations
Booth, Richard UL; Chevaleyre, Yann; Lang, Jérôme et al

Scientific Conference (2011)

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See detailBelief change
Booth, Richard UL; Meyer, Thomas

in Journal of Indian Council of Philosophical Research (2011), 27

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See detailQuantifying disagreement in argument-based reasoning
Booth, Richard UL; Caminada, Martin UL; Podlaszewski, Mikołaj UL et al

Scientific Conference (2011)

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See detailOn the Link between Partial Meet, Kernel, and Infra Contraction and its Application to Horn Logic
Booth, Richard UL; Meyer, Thomas; Varzinczak, Ivan José et al

in Journal of Artificial Intelligence Research (2011), 42

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See detailLearning conditionally lexicographic preference relations
Booth, Richard UL; Chevaleyre, Yann; Lang, Jérôme et al

in Proceedings of the 19th European Conference on Artificial Intelligence (ECAI 2010) (2010)

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