Connecting lexicographic with maximum entropy entailment

Abstract. This paper reviews and relates two default reasoning mechanisms, lexicographic (lex) and maximum entropy (me)entailment. Meentailment requires that defaults be assigned speci c strengths and it is shown that lex-entailment can be equated to me-entailment for a class of speci c strength assignments. By clarifying the assumptions which underlie lex-entailment, it is argued that me-entailment is a superior method of handling default inference for reasons of both expressiveness and objective justi cation.

For the sake of the Argument : explorations into argument-based reasoning

Riet, R.P. van de [Promotor]Prakken, H. [Copromotor

Tracking and judging debates using argumentation.

Using argumentation to debate and reach conclusions is a particularly human activity relevant to many professions and applications. Debates exist not only in the Houses of Parliament, but also in such disciplines as medicine and law. In this theoretical thesis I explore three new logical constructs for realistic debate modelling, namely: confirmation, preclusion and reflection. Confirmation is two or more arguments for a claim, used to provide corroboration of evidence. Preclusion is an attacking argument that says 'one or other of your arguments is wrong' an argumentation technique used adeptly by Sherlock Holmes and many politicians. Reflection is a way of identifying logical redundancies (i.e. predictable patterns) in the argument data structure of a debate. A reflection originates from an unpredictable 'reflector' argument and gives rise to the predictable or 'reflected' argument. One type of reflection can be said to 'flow down' a tree of arguments, where the reflector is nearer the root and the reflected arguments further from the root, while another kind 'flows up' the tree in the reverse direction. Incorporating preclusion into the model of reflection increases this to four distinct types of reflection, two up-tree and two down-tree. The value of identifying and removing reflections is to ensure intuitive, or arguably 'correct', results when judging debates, be that judgement based on the existence or number of arguments. Re moving reflection also aids human comprehension of the debate as it reduces the number of arguments involved. This logical analysis of reflection and preclusion leads to the definition of a reflection-free, preclusion-aware, debate-tracking tree. Finally, the framework addresses judging the tree to determine who won the debate, with a proposal that takes confirmation into account when reaching conclusions. Confirmation assessment is helpful in resolving inconsistencies. Out of scope are notions of alternating moves by competing players and computational complexity