Challenges of Formal Commonsense Reasoning

A Logicistic Perspective

In previous posts (Philosophical Definitions of Commonsense, On Logicism and Commonsense, Montague Grammar, Commonsense Reasoning), I already sketched some considerations regarding the current state of commonsense reasoning as inspired mostly by Davis and Morgenstern. Here, I’d like to emphasise more explicitly the challenges that are entailed by the application of the logicism methodology.

Logicist Agenda in Practice

Logicism of a certain topic consists of the following two sides:

L.1 An axiomatic theory of the given topic,
L.2 deduction rules given by logic.

First, a powerful formal language has to be designed that has to represent encountered facts as a sound axiomatic theory. Furthermore, it needs to allow manipulation of inherent truths and allows inferences as given by the mentioned deduction rules.

For commonsense, the goal of this logicist theory is to create a language that expresses adequately the patterns we can find in commonsense knowledge/beliefs and commonsense reasoning. Moreover, not only the patterns but also the content or inherent meaning of commonsense knowledge and beliefs must be expressed in a precise way.

The second task of logicism is to go through this formalization to demonstrate its adequacy. This means in practical terms that a sole idea is not sufficient but a full-fleshed theory is necessary: inconsistencies and issues usually reveal themselves through application.

Moreover, when defining the necessary commonsense knowledge and beliefs, a database is needed for a commonsense theory. Going through this formalisation would mean organising this huge number of commonsense facts such that together with the logical axioms, it has to represent our understanding of commonsense and the knowledge is also usable in an efficient way.

Philosophical Parallels

Combining these two levels would combine also partially the different philosophical aspects:

To recall the first school, I mentioned defines commonsense as our critical faculties of judgment. This is represented by L.2, the deduction rules of the given logics.

On the other hand, we have common beliefs, principles that we take for granted in common life without the capability to reason for them. We can store those in a database with the same representational formal language. The universality of such beliefs can then be taken as the theory L.1.

Finally, by collecting a huge number of uttered facts in a linguistic community, we obtain a good approximation of the collective sense of society. This refers to concepts and ideas shared by the whole linguistic community. Therefore, it represents those parts of the everyday language that arise from cultural evolution.

Sources

Ernest Davis and Leora Morgenstern. 2004. Introduction: Progress in formal commonsense reasoning. Artificial Intelligence, 153(1–2):1–12.