On Logicism and Commonsense

Reviews on formal Semantics and Commonsense

In this post, I already introduced the philosophical traditions regarding commonsense. While commonsense reasoning is an ongoing research topic in natural language processing, there is an older approach to it that fits better some of those philosophical schools: the approach consists of deriving formal semantics from linguistic logicism. However, before going into the linguistic part, I’d like to discuss first the relationship between logicism and commonsense.

Logicist Methodology

The methodology of logicism itself was already discussed in a lot of works. I think Thomason gave an intuitive approach to its concrete execution. Let me rephrase first its two parts:

L.1 an axiomatic theory of the given topic,

L.2 deduction rules given by logic.

To be formulated in such a way, the logicism of a specific topic must adequately represent it. This approach then rests on finding the corresponding patterns that express the topic. Furthermore, one has to go through with its formalisation as a demonstration of its adequacy.

Nevertheless, the first results of this philosophical approach were mainly applied to mathematics as an attempt to formalise its foundation of it. For its application to discipline in the empirical domain, it’s rather problematic to find a suitable formalism when incomplete results (Incompleteness in mathematical logic refers to Gödel’s theorems that describe the limitations of formal systems that model basic arithmetic. They essentially prove that such a system contains improbable but nonetheless true statements. Furthermore, it cannot prove its own consistency.) limited adequacy of this approach.

Critical Faculties

At this point, it might be already interesting to mention the parallels between logicism and the previous philosophical considerations in mylast post.

To recall the first school, I mentioned defines commonsense as our critical faculties of judgment. More concretely, it is assumed that everyone regardless of region and time period the person lives in possesses the same capabilities of judgement as given by birth. So it means that commonsense is a universal phenomenon.

Especially the second point L.2 deduction rules given by logic can be seen as rules of judgement on how to correctly infer knowledge in the given context. When assuming that commonsense consists of universal rules, we could use logic adequately to objectify it in such a way.

Common Beliefs

Opposing the idea of defining commonsense solely as critical faculties, commonsense can be defined as universal beliefs that rather complement the natural capabilities we receive at birth. So it does not represent knowledge everyone achieves through critical judgement but rather principles that we take for granted in the common life without the capability to reason for it.

Depending on how broadly we understand the term “axiomatic theory” as in L.1, the universality of common beliefs can be seen as a set of basic facts necessary to build an actual axiomatic theory. Similarly, to these beliefs, as mentioned earlier, we also don’t derive axioms from any underlying facts. We often take them for granted as underlying principles.

Concluding Remarks

Taking the two philosophical schools together, the complementary and interdependent nature of critical faculties and common beliefs seem to behave like the relationship between L.1 and L.2. Therefore, from these two philosophical aspects, the logicist methodology seems adequate for expressing a formal theory of commonsense.

Nevertheless, it is worth mentioning that this “set of common beliefs” is not exclusive to an axiomatic theory in logicism but can be included in different approaches to commonsense (e.g., machine learning).

Linguistic logicism is then a special case of logicism. This approach than actually formalises the logistic method for language and consequently also allows for a logicist foundation of commonsense. But that’s a topic for upcoming posts.

Sources

Richmond H. Thomason. 1991. Logicism, artificial intelligence, and common sense. Artificial Intelligence and Mathematical Theory of Computation: papers in honor of John McCarthy, pages 449–466.

Richmond H. Thomason. 1996. Logicism in formalizing common sense and in natural language semantics. In Proceedings of Common Sense ’96, Third
Symposium on Logical Formalizations of Commonsense Reasoning.