From truth to computability I

The recently initiated approach called computability logic is a formal theory of interactive computation. See a comprehensive online source on the subject at http://www.cis.upenn.edu/~giorgi/cl.html . The present paper contains a soundness and completeness proof for the deductive system CL3 which axiomatizes the most basic first-order fragment of computability logic called the finite-depth, elementary-base fragment. Among the potential application areas for this result are the theory of interactive computation, constructive applied theories, knowledgebase systems, systems for resource-bound planning and action. This paper is self-contained as it reintroduces all relevant definitions as well as main motivations.Comment: To appear in Theoretical Computer Scienc

Subjective Logic and Arguing with Evidence

Peer reviewedPreprin

The interaction of representation and reasoning

Automated reasoning is an enabling technology for many applications of informatics. These applications include verifying that a computer program meets its specification; enabling a robot to form a plan to achieve a task and answering questions by combining information from diverse sources, e.g. on the Internet, etc. How is automated reasoning possible? Firstly, knowledge of a domain must be stored in a computer, usually in the form of logical formulae. This knowledge might, for instance, have been entered manually, retrieved from the Internet or perceived in the environment via sensors, such as cameras. Secondly, rules of inference are applied to old knowledge to derive new knowledge. Automated reasoning techniques have been adapted from logic, a branch of mathematics that was originally designed to formalize the reasoning of humans, especially mathematicians. My special interest is in the way that representation and reasoning interact. Successful reasoning is dependent on appropriate representation of both knowledge and successful methods of reasoning. Failures of reasoning can suggest changes of representation. This process of representational change can also be automated. We will illustrate the automation of representational change by drawing on recent work in my research group

Meta-level argumentation framework for representing and reasoning about disagreement

The contribution of this thesis is to the field of Artificial Intelligence (AI), specifically to the sub-field called knowledge engineering. Knowledge engineering involves the computer representation and use of the knowledge and opinions of human experts.In real world controversies, disagreements can be treated as opportunities for exploring the beliefs and reasoning of experts via a process called argumentation. The central claim of this thesis is that a formal computer-based framework for argumentation is a useful solution to the problem of representing and reasoning with multiple conflicting viewpoints.The problem which this thesis addresses is how to represent arguments in domains in which there is controversy and disagreement between many relevant points of view. The reason that this is a problem is that most knowledge based systems are founded in logics, such as first order predicate logic, in which inconsistencies must be eliminated from a theory in order for meaningful inference to be possible from it.I argue that it is possible to devise an argumentation framework by describing one (FORA : Framework for Opposition and Reasoning about Arguments). FORA contains a language for representing the views of multiple experts who disagree or have differing opinions. FORA also contains a suite of software tools which can facilitate debate, exploration of multiple viewpoints, and construction and revision of knowledge bases which are challenged by opposing opinions or evidence.A fundamental part of this thesis is the claim that arguments are meta-level structures which describe the relationships between statements contained in knowledge bases. It is important to make a clear distinction between representations in knowledge bases (the object-level) and representations of the arguments implicit in knowledge bases (the meta-level). FORA has been developed to make this distinction clear and its main benefit is that the argument representations are independent of the object-level representation language. This is useful because it facilitates integration of arguments from multiple sources using different representation languages, and because it enables knowledge engineering decisions to be made about how to structure arguments and chains of reasoning, independently of object-level representation decisions.I argue that abstract argument representations are useful because they can facilitate a variety of knowledge engineering tasks. These include knowledge acquisition; automatic abstraction from existing formal knowledge bases; and construction, rerepresentation, evaluation and criticism of object-level knowledge bases. Examples of software tools contained within FORA are used to illustrate these uses of argumentation structures. The utility of a meta-level framework for argumentation, and FORA in particular, is demonstrated in terms of an important real world controversy concerning the health risks of a group of toxic compounds called aflatoxins