Nikos Gorogiannis

Instantiating abstract argumentation with classical logic arguments: Postulates and properties

In this paper we investigate the use of classical logic as a basis for instantiating abstract argumentation frameworks. In the first part, we propose desirable properties of attack relations in the form of postulates and classify several well-known attack relations from the literature with regards to the satisfaction of these postulates. Furthermore, we provide additional postulates that help us prove characterisation results for these attack relations. In the second part of the paper, we present postulates regarding the logical content of extensions of argument graphs that may be constructed with classical logic. We then conduct a comprehensive study of the status of these postulates in the context of the various combinations of attack relations and extension semantics.

A Generic Cyclic Theorem Prover

We describe the design and implementation of an automated theorem prover realising a fully general notion of cyclic proof. Our tool, called (textsc{Cyclist}), is able to construct proofs obeying a very general cycle scheme in which leaves may be linked to any other matching node in the proof, and to verify the general, global infinitary condition on such proof objects ensuring their soundness. (textsc{Cyclist}) is based on a new, generic theory of cyclic proofs that can be instantiated to a wide variety of logics. We have developed three such concrete instantiations, based on: (a) first-order logic with inductive definitions; (b) entailments of pure separation logic; and (c) Hoare-style termination proofs for pointer programs. Experiments run on these instantiations indicate that (textsc{Cyclist}) offers significant potential as a future platform for inductive theorem proving.

Implementing semantic merging operators using binary decision diagrams

There is a well-recognised need in diverse applications for reasoning with multiple, potentially inconsistent sources of information. One approach is to represent each source of information by a set of formulae and then use a merging operator to produce a set of formulae as output. A valuable range of model-based operators have been proposed that conform to interesting and intuitive properties. However, the implementation of such operators has remained unaddressed, partly due to the considerable computational complexity of the proposals. To address this, we propose a methodology for implementing model-based merging operators using the notion of dilation and a type of data structure called a binary decision diagram. We apply this method by implementing four merging operators from the literature and experimentally evaluating their average-case performance. The results indicate that while the complexity is indeed significant, problems of modest size can be treated using commodity hardware and short computation times.

An argument-based approach to reasoning with clinical knowledge

Better use of biomedical knowledge is an increasingly pressing concern for tackling challenging diseases and for generally improving the quality of healthcare. The quantity of biomedical knowledge is enormous and it is rapidly increasing. Furthermore, in many areas it is incomplete and inconsistent. The development of techniques for representing and reasoning with biomedical knowledge is therefore a timely and potentially valuable goal. In this paper, we focus on an important and common type of biomedical knowledge that has been obtained from clinical trials and studies. We aim for (1) a simple language for representing the results of clinical trials and studies; (2) transparent reasoning with that knowledge that is intuitive and understandable to users; and (3) simple computation mechanisms with this knowledge in order to facilitate the development of viable implementations. Our approach is to propose a logical language that is tailored to the needs of representing and reasoning with the results of clinical trials and studies. Using this logical language, we generate arguments and counterarguments for the relative merits of treatments. In this way, the incompleteness and inconsistency in the knowledge is analysed via argumentation. In addition to motivating and formalising the logical and argumentation aspects of the framework, we provide algorithms and computational complexity results.

Merging first-order knowledge using dilation operators

The area of knowledge merging is concerned with merging conflicting information while preserving as much as possible. Most proposals in the literature work with knowledge bases expressed in propositional logic. We propose a new framework for merging knowledge bases expressed in (subsets of) first-order logic. Dilation operators (a concept originally introduced by Bloch and Lang) are employed and developed, and by combining them with the concept of comparison orderings we obtain a framework that is driven by model-based intuitions but that can be implemented in a syntax-based manner. We demonstrate specific dilation operators and comparison orderings for use in applications. We also show how postulates from the literature on knowledge merging translate into our framework and provide the conditions that dilation operators and comparison orderings must satisfy in order for the respective merging operators to satisfy the new postulates.

The Complexity of the Warranted Formula Problem in Propositional Argumentation

The notion of warrant or justification is one of the central concepts in formal models of argumentation. The dialectical definition of warrant is expressed in terms of recursive defeat: an argument is warranted if each of its counter-arguments is itself defeated by a warranted counter-argument. However, few complexity results exist on checking whether an argument is warranted in the context of deductive models of argumentation, i.e. models where an argument is a deduction of a claim from a set of premises using some logic. We investigate the computational complexity of checking whether a claim is warranted in propositional argumentation under two natural definitions of warrant and show that it is PSPACE-complete in both cases.

Argumentation about treatment efficacy

The volume and complexity of knowledge produced by medical research calls for the development of technology for automated management and analysis of such knowledge. In this paper, we identify scenarios where a researcher or a clinician may wish to use automated systems for analysing knowledge from clinical trials. For this, we propose a language for encoding, capturing and synthesising knowledge from clinical trials and a framework that allows the construction of arguments from such knowledge. We develop this framework and demonstrate its use on a case study regarding chemotherapy regimens for ovarian cancer.

The complexity of abduction for separated heap abstractions

Abduction, the problem of discovering hypotheses that support a conclusion, has mainly been studied in the context of philosophical logic and Artificial Intelligence. Recently, it was used in a compositional program analysis based on separation logic that discovers (partial) pre/post specifications for un-annotated code which approximates memory requirements. Although promising practical results have been obtained, completeness issues and the computational hardness of the problem have not been studied. We consider a fragment of separation logic that is representative of applications in program analysis, and we study the complexity of searching for feasible solutions to abduction. We show that standard entailment is decidable in polynomial time, while abduction ranges from NP-complete to polynomial time for different sub-problems.