aspg-34-1469-1791482507 20261008180147 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group Prospects for Applied Mathematics and Data Analysis PAMDA 2836-4449 2023 1 1 Adel Mohammed Al-Odhari Department of Mathematics Faculty of Education, Humanities and Applied Sciences – khawlan Sana'a University. Box:13509, Sana'a, Yemen In this paper, we devoted to study the language monadic predicate logic system plus identity (LMPLS+I) as extension of the language of propositional logic system (LPLS). I.e., ( style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-fareast-font-family:"Cambria Math";mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi'>LPLS)⊂ o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> height:12.75pt'> o:title="" chromakey="white"/> (LMPLS+I), which it contains all the hereditary traits (or features) of style='mso-bidi-font-style:normal'> "Cambria Math",serif;mso-fareast-font-family:"Cambria Math";mso-bidi-font-family: "Times New Roman";mso-bidi-theme-font:major-bidi'>(LPLS) style='width:30.75pt;height:12.75pt'> o:title="" chromakey="white"/> , furthermore that, we will add some new data information between relationship of object, subject and predicate. This is the task of monadic predicate logic system addressed. As mentioned in pervious papers, the main task of system of logic is classifying between valid and invalid arguments, moreover, the central role the system of logic how distinguishes between the conclusions which follow from their premises of the arguments and those do not follow from their premises. As a matter of fact, when we encounter some proofs that seem perceptually (or intuitively) sound, but we are -unable to prove their validity due to the inability language of propositional logic system (LPLS). Hence, it was necessary to uses the monadic predicate logic system (LMPLS+I) to overcome this problem. In this article, we study syntax, semantics and inference on language monadic predicate logic system plus identity (LMPLS+I) and investigation characteristics of arguments such valid \ invalid and types of formulas and relations between formulas like consistency and inconsistency sets. 2023 31 51 1469 https://creativecommons.org/licenses/by/4.0/ 10.54216/PAMDA.010103 https://www.americaspg.com/journal/34/article/1469 https://www.americaspg.com/storage/71701032477.pdf