Alexander Bochman

Computer Science Department, Holon Institute of Technology, Israel

August 1st, 14:00-15;30 (part1), 16;00-17:30 (part2)

https://easychair.org/smart-program/FLoC2022/ABR-index.html

Description

The aim of the tutorial is to provide a gentle introduction to Assumption-Based Reasoning (ABR) which will be argued to constitute the core of Nonmonotonic

Reasoning in AI. The tutorial is planned for half a day. After a brief overview of nonmonotonic reasoning in AI, we will focus on default logic [Reiter, 1980] and show first that it can be reformulated as a logical formalism containing only plain inference rules and default assumptions (see [Bochman, 2008]). Then we introduce a general bipolar framework of Assumption Based Reasoning that contains two kinds of propositions: facts and assumptions. The difference between the two is based on their different, opposite acceptability status: while facts are accepted only if we have reasons (or causes) for their acceptance, assumptions are always accepted unless we have reasons for their rejection or cancellation.

As a next step, we will consider Dung’s argumentation theory [Dung, 1995] and show that it can be viewed as a general, abstract theory of assumptions. We will show also how this abstract theory can be extended to a full-fledged bipolar reasoning formalism about facts and assumptions by augmenting its underlying logic (see [Bochman, 2017]). This extension will also be shown to be closely correlated with Assumption Based Argumentation (ABA) (see [Bondarenko et al., 1997]) that subsumes, in turn, the main nonmonotonic formalisms in AI.

As far as the time will permit, we will describe also a general theory of causal reasoning that can be viewed as yet another instantiation of assumption-based

reasoning; in this instantiation, causal rules will function as assumptions (see [Bochman, 2021]).

Toward the end, we will discuss the consequences and prospects created by this novel perspective on nonmonotonic reasoning in AI.

Outline of the tutorial

• What is a nonmonotonic reasoning?

• Default logic and its assumption-based reformulation.

• Assumption-based reasoning (ABR): a bipolar reasoning about acceptance and rejection of propositions.

• Dung’s argumentation theory as an abstract theory of assumptions and its extension to full ABR.

• Causal reasoning as an ABR.

• Summary and prospects.

Suggested Reading

[Bochman, 2005] A. Bochman Explanatory Nonmonotonic Reasoning. World Scientific. 2005

[Bochman, 2008] A. Bochman. Default logic generalized and simplified. Annals of Mathematics and Artificial Intelligence, 53:21–49, 2008.

[Bochman, 2017] Alexander Bochman. Argumentation, Nonmonotonic Reasoning and Logic. FLAP, 4(8), 2017.

[Bochman, 2021] A. Bochman. A Logical Theory of Causality. MIT Press, 2021.

[Bondarenko et al., 1997] A. Bondarenko, P. M. Dung, R. A. Kowalski, and F. Toni. An abstract, argumentation-theoretic framework for default reasoning.

Artificial Intelligence, 93:63–101, 1997.

[Dung, 1995] P. M. Dung. On the acceptability of arguments and its fundamental role in non-monotonic reasoning, logic programming and n-persons games.

Artificial Intelligence, 76:321–358, 1995.

[Reiter, 1980] R. Reiter. A logic for default reasoning. Artificial Intelligence, 13:81–132, 1980.