# Non-Axiomatic Logic Modeling of English Texts for Knowledge Discovery and Commonsense Reasoning
## 1 Introduction  
Endowing artificial agents with the ability to understand natural language in a way similar to humans is a task in which artificial intelligence has not yet made enough progress [1, 2, 3]. Even the most advanced connectionist and generative models, trained with gigabytes of examples and on large-scale high-performance clusters, perform poorly when faced with the task of commonsense reasoning based on the contents of natural language texts [4, 5]. From the symbolic perspective, modeling natural language with logic has also yielded poor results, but it is believed that those poor results are a consequence of the low expressive power of the logics used for modeling [6, 7]. When predicate logic (PL) or any of its subsets have been used, poor results are also attributed to the mathematical orientation of those logics as well as their inability to model everyday concept acquisition and processing [8, 9]. If a radically different logic is used, it may be possible to obtain better results, and that is exactly the case with non-axiomatic logic (NAL), a formal language designed to model the process of an agent pragmatically learning its environment [10, 11]. As such, NAL offers several advantages over other symbolic logics [12, 13], such as the ability to define higher-order expressions and use a variety of inference models besides deduction. Although similar studies have been published using different logics, and even some of them have used the exact same logic (NAL), in all of them the core problem is the same:translating natural language expressions into a formal language. Previous efforts in other logics have focused on formulating syntactic methods for identifying grammatical structure and semantic roles, but since we believe there is no clear, universal and deterministic way of doing so, in this research, we proceed the other way around. We use linguistic analysis tools to provide the grammatical and semantic elements needed for constructing an equivalent logic expression and provide context for each concept by using a general purpose ontology (WordNet). The main contributions of this paper can be summarized as follows:  
1. We reverse the traditional process of tackling the problem of natural language translation into formal language by selecting some linguistic analysis tools as a guide for constructing logic expressions with approximately the same semantics as the natural language sentences being translated. 2. We use a logic that has features that other classic logics lack: subject-predicate sentences, experience-grounded semantics and syllogistic inference rules [14]. In contrast with the other representations of NL in NAL, our proposal have the following novelties:  
1. We predefined some NAL terms (concepts), as well as some NAL term relations, for representing grammatical and semantic relations commonly found in English sentences. 2. We propose a set of NL-to-NAL translation rules general enough to cover the great majority of English universal dependencies use cases and provide a full set of examples. 3. We include not only grammatical properties of the translated sentences but semantic elements too. 4. Finally, we glimpse into the possible use of the proposed translation rules for supporting commonsense reasoning tasks [15]. The rest of this article is organized as follows: In Section 2, (Related Work) we briefly mention some previous related works that are relevant in understanding our contribution, either because of the similarity of the ideas used or because of the opposite. In Section 3, (Theoretical Foundations and Required Background Knowledge) the fundamental basic concepts of NAL are presented, as well as a brief listing of the linguistic tools used in this research. Section 4 (Proposal) details our proposal for translating English sentences into NAL expressions, including the predefined terms and their semantics, as well as the predefined relations used during the translation process.