## Institut für Informatik und Computational Science

Formalizing informal logic
(2015)

In this paper we investigate the extent to which formal argumentation models can handle ten basic characteristics of informal logic identified in the informal logic literature. By showing how almost all of these characteristics can be successfully modelled formally, we claim that good progress can be made toward the project of formalizing informal logic. Of the formal argumentation models available, we chose the Carneades Argumentation System (CAS), a formal, computational model of argument that uses argument graphs as its basis, structures of a kind very familiar to practitioners of informal logic through their use of argument diagrams.

This document presents an axiom selection technique for classic first order theorem proving based on the relevance of axioms for the proof of a conjecture. It is based on unifiability of predicates and does not need statistical information like symbol frequency. The scope of the technique is the reduction of the set of axioms and the increase of the amount of provable conjectures in a given time. Since the technique generates a subset of the axiom set, it can be used as a preprocessor for automated theorem proving. This technical report describes the conception, implementation and evaluation of ARDE. The selection method, which is based on a breadth-first graph search by unifiability of predicates, is a weakened form of the connection calculus and uses specialised variants or unifiability to speed up the selection. The implementation of the concept is evaluated with comparison to the results of the world championship of theorem provers of the year 2012 (CASC J6). It is shown that both the theorem prover leanCoP which uses the connection calculus and E which uses equality reasoning, can benefit from the selection approach. Also, the evaluation shows that the concept is applyable for theorem proving problems with thousands of formulae and that the selection is independent from the calculus used by the theorem prover.