Logic: Syntax and Semantics

Syllogism vs. symbolic logic vs. mathematical logic we distinguish the informal study of patterns of argument (fallacies, etc.), the study of formal terms and their meaning, and the study of meta-theoretical properties of formal systems

Logic: Syntax and Semantics

	Syllogism vs. symbolic logic vs. mathematical logic
	Propositional calculus the simplest (algebraic!) form of logic includes abstract propositions (truth-bearing tokens represented by symbols or variables) and simple operators (negation, conjunction, disjunction, implication)

Logic: Syntax and Semantics

	Syllogism vs. symbolic logic vs. mathematical logic
	Propositional calculus
	Syntax and semantics the syntactic and semantic aspects to propositional logic are then expressed in terms of (e.g.) proof trees for the derivability and truth tables for consequence

Logic: Syntax and Semantics

	Syllogism vs. symbolic logic vs. mathematical logic
	Propositional calculus
	Syntax and semantics
	Predicate calculus and first-order logic a more sophisticated (finer, richer) analysis of reasoning identifies individuals and predicates (i.e., properties), then allows quantification over formulae (note: quantification binds variables)

Logic: Syntax and Semantics

	Syllogism vs. symbolic logic vs. mathematical logic
	Propositional calculus
	Syntax and semantics
	Predicate calculus and first-order logic
	Proof theory and model theory meta-theoretical studies then address such issues as coherence (between syntax and semantics) or how finely or coarsely a theory can characterize possible models

Logic: Syntax and Semantics

	Syllogism vs. symbolic logic vs. mathematical logic
	Propositional calculus
	Syntax and semantics
	Predicate calculus and first-order logic
	Proof theory and model theory
	Non-standard logics in addition to classical first-order logic, people study: • second-order logic (allows quantification over properties and functions); • intuitionistic logic (denies the excluded middle, forcing constructive proofs); • relevance logic (ties antecedents and consequents together more deeply); • modal logic (models notions of possibility and necessity).