Three Dogmas, a Puzzle and its Solution (2310.19123v1)

Abstract: Modern Logics, as formulated notably by Frege, Russell and Tarski involved basic assumptions about Natural Languages in general and Indo-European Languages in particular, which are contested by Linguists. Based upon those assumptions, formal Languages were designed to overcome what Logicians claimed to be 'defects' of Natural Language. In this paper we show that those assumptions contradict basic principles of Arabic. More specifically: The Logicians ideas, that within Natural Language words refer to objects, 'ToBe'-constructions represent identity statements, Indefinite Descriptions must be replaced by existential quantifiers to form meaningful Sentences and Symbols can have no interpretation-independent meanings, are all falsified using undisputed principles of Arabic. The here presented falsification serves two purposes. First, it is used as a factual basis for the rejection of approaches adopting Semantic axioms of Mathematical Logics as Models for meaning of Arabic Syntax. Second, it shows a way to approach the important computational problem: Satisfiability (SAT). The described way is based upon the realization that parsing Arabic utilizes the existence of 'meaning-particles' within Syntax to efficiently recognize words, phrases and Sentences. Similar meaning-particles are shown to exist in 3CNF formulas, which, when properly handled within the machinery of 3SAT-Solvers, enable structural conditions to be imposed on formulas, sufficient alone to guarantee the efficient production of non-exponentially sized Free Binary Decision Diagrams (FBDDs). We show, why known exponential Lower Bounds on sizes of FBDDs do not contradict our results and reveal practical evidence, obtained for multiplication circuits, supporting our claims.