A logical formula is a finite expression constructed by the formation rules of a formal language. Propositional formulas combine propositional variables by logical connectives. First-order formulas additionally contain terms, atomic relations and quantifiers. A logical formula is a syntactic object; its truth is determined only after specifying a suitable interpretation and values for its free variables.
A logical variable is a symbol whose value is supplied by the semantics of a logical language. A propositional variable receives a truth value under a Boolean valuation. An individual variable of first-order logic receives an element of a structure under an assignment. These are different kinds of variable and should not be identified.
Ancestors (5)
Incoming links (87)
- Arithmetical proof relation
- Canonical models of complete theories are prime
- Class term
- Complete omega-consistent arithmetic theories are sound
- Finite transitive counterexample for power-set equality
- Finite-tuple homogeneity
- Logical formula
- Morleyization
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- Prefix-freeness of fully parenthesized formulas
- Principal complete type
- Principal formula of a type
- Propositional consistency
- Replacement in the well-founded part
- Replacement theorem for logical equivalence
- Strong definability of a numerical function
- Subformula occurrence
- Subformula replacement
- Subformula replacement theorem
- Symbol interpretation in a first-order structure
- Syntax tree of a formula
- Theoremhood
- Theory of a free bijection
- Types realized in finite structures are principal
- Unique readability theorem
- Universal sentences are preserved by substructures
- Weak definability of a numerical function
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