Which formal system deals with predicates and quantifiers across mathematics, philosophy, linguistics, and computer science?

• A. First Order Predicate Logic
• B. Propositional Logic
• C. Modal Logic
• D. Lambda Calculus

Answer: (A)

Reasoning about objects, their properties, and how many of them exist is captured by a formal system that uses predicates and quantifiers. First Order Predicate Logic lets you state things like “for every object x, P(x) holds” or “there exists an object x such that Q(x).” It combines predicates (properties and relations) with universal and existential quantifiers, plus variables, to express meaningful statements about mathematics, philosophy, linguistics, and computer science.

Propositional logic only deals with whole statements and their connectives, without talking about properties of individual objects or how many objects satisfy a condition. Modal logic adds notions like necessity and possibility, which isn’t the primary tool for expressing general quantification over objects. Lambda calculus focuses on functions and computation rather than the logical vocabulary needed to talk about objects, properties, and their relationships across those disciplines.

So the formal system that best covers predicates and quantifiers across mathematics, philosophy, linguistics, and computer science is the first order predicate logic.