Formal semantics

Formal semantics assigns mathematical objects or conditions to expressions in a formal language. It makes meaning precise enough to analyze properties such as truth, validity, and program behavior.

Formal language: A set of strings defined over an alphabet by rules or constraints. Semantics assigns meaning to expressions drawn from a formally specified language.
Tarskian semantics: A model-theoretic approach defining truth for formal languages through satisfaction in a structure. It gives a precise recursive account of when logical sentences hold in models.
Hoare logic: A formal system for reasoning about programs using assertions before and after commands. Its program-correctness claims rely on a semantics for commands and states.
Natural language semantics: The study of how natural-language expressions convey meaning and support interpretation. Unlike formal-language semantics, it must account for ambiguity, context, and linguistic variation.
Syntax: Rules governing how symbols combine into well-formed expressions. Syntax determines which expressions receive interpretations.
Denotational semantics: A method for defining programming-language constructs as mathematical objects, often functions or domains. It assigns program phrases compositional mathematical denotations.
Type system: Rules that assign types to expressions and constrain their permitted uses. Semantic models help explain why well-typed programs satisfy safety properties.
Pragmatics: The study of how context and communicative use affect utterance interpretation. It addresses aspects of communicated meaning that formal truth conditions may leave aside.
Interpretation: A mapping that assigns meanings or denotations to expressions in a formal language. It is the central mathematical act that turns formal expressions into meanings.
Operational semantics: A method that defines program meaning through rules describing computation steps or outcomes. It characterizes programs by execution behavior rather than denotations.

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