Lakatos-Style Automated Theorem Modification

Lakatos-style Methods in Automated Reasoning

A computational model of Lakatos-style reasoning

Lakatos outlined a theory of mathematical discovery and justification, which suggests ways in which concepts, conjectures and proofs gradually evolve via interaction between mathematicians. Different mathematicians may have different interpretations of a conjecture, examples or counterexamples of it, and beliefs regarding its value or theoremhood. Through discussion, concepts are refined and co...

Lakatos-style collaborative mathematics through dialectical, structured and abstract argumentation

The simulation of mathematical reasoning has been a driving force throughout the history of Artificial Intelligence research. However, despite significant successes in computer mathematics, computers are not widely used by mathematicians apart from their quotidian applications. An oft-cited reason for this is that current computational systems cannot do mathematics in the way that humans do. We...

Representation Theorems and Theorem Proving in Non-Classical Logics

In this paper we present a method for automated theorem proving in non-classical logics having as algebraic models bounded distributive lattices with certain types of operators. The idea is to use a Priestley-style representation for distributive lattices with operators in order to define a class of Kripke-style models with respect to which the logic is sound and complete. If this class of Krip...

Applying Lakatos-style reasoning to AI problems

Lakatos (1976) argued that mathematics develops in a much more organic way than its rigid textbook presentation of definition-theorem-proof would suggest. He outlined a heuristic approach which holds that mathematics progresses by a series of primitive conjectures, proofs, counterexamples, proof-generated concepts, modified conjectures and modified proofs. The purpose of this chapter is to appl...