Formalizing Sense Relations in Sentence Level from Logical Point of View: A Study of Mathematical Linguistics

The present paper studies the possibility of translating “sense relations” in the level of sentences into formal expressions. In so doing, it applies the mathematical logic, especially the logic of propositions within the constraints of sufficient Farsi examples. That is, firstly, a definition for each relation in sentence level is presented. Secondly, using the tools of propositional logic, a formal translation for each relation is offered. Then, each of the proposed relation is shown to be in accordance with its corresponding sense relation; finally, the efficiency of the formal expression is tested by examples from Farsi. The sense relations discussed are as follows: entailment, contradiction, inference, and presupposition. The author concluded that the sense relation of “synonymy” is, basically, impossible to be translated into formal expression since there are no two sentences in any language that can be considered “synonymous”. Thus, no formal translation can be proposed for “synonymy” in the sentence level.