Knowledgebase Compilation for Efficient Logical Argumentation

There are a number of frameworks for modelling argumentation in logic. They incorporate a formal representation of individual arguments and techniques for comparing conflicting arguments. A common assumption for logic-based argumentation is that an argument is a pair 〈Φ,α 〉 where Φ is minimal subset of the knowledgebase such that Φ is consistent and Φ entails the claim α. Different logics are based on different definitions for entailment and consistency, and give us different options for argumentation. For a variety of logics, in particular for classical logic, the computational viability of generating arguments is an issue. Here, we present a solution that involves compiling a knowledgebase ∆ based on the set of minimal inconsistent subsets of ∆, and then generating arguments from the compilation. Whilst generating a compilation is expensive, generating arguments from a compilation is relatively inexpensive

Algorithms for computational argumentation in artificial intelligence

Argumentation is a vital aspect of intelligent behaviour by humans. It provides the means for comparing information by analysing pros and cons when trying to make a decision. Formalising argumentation in computational environment has become a topic of increasing interest in artificial intelligence research over the last decade. Computational argumentation involves reasoning with uncertainty by making use of logic in order to formalize the presentation of arguments and counterarguments and deal with conflicting information. A common assumption for logic-based argumentation is that an argument is a pair where Φ is a consistent set which is minimal for entailing a claim α. Different logics provide different definitions for consistency and entailment and hence give different options for formalising arguments and counterarguments. The expressivity of classical propositional logic allows for complicated knowledge to be represented but its computational cost is an issue. This thesis is based on monological argumentation using classical propositional logic [12] and aims in developing algorithms that are viable despite the computational cost. The proposed solution adapts well established techniques for automated theorem proving, based on resolution and connection graphs. A connection graph is a graph where each node is a clause and each arc denotes there exist complementary disjuncts between nodes. A connection graph allows for a substantially reduced search space to be used when seeking all the arguments for a claim from a given knowledgebase. In addition, its structure provides information on how its nodes can be linked with each other by resolution, providing this way the basis for applying algorithms which search for arguments by traversing the graph. The correctness of this approach is supported by theoretical results, while experimental evaluation demonstrates the viability of the algorithms developed. In addition, an extension of the theoretical work for propositional logic to first-order logic is introduced

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