On the Entailment Problem for a Logic of Typicality

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 ▲]

A logical theory about dynamics in abstract argumentation

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 ▲]

A logical theory about dynamics in abstract argumentation

Scientific Conference (2013)

Monotonic and non-monotonic inference for abstract argumentation

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 ▲]

PTL: A propositional typicality logic

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

Credibility-limited revision operators in propositional logic

Scientific Conference (2012)

Quantifying disagreement in argument-based reasoning

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 ▲]

On the Link between Partial Meet, Kernel, and Infra Contraction and its Application to Horn Logic

in Journal of Artificial Intelligence Research (2011), 42

How to revise a total preorder

in Journal of Philosophical Logic (2011), 40

Learning conditionally lexicographic preference relations

Scientific Conference (2011)