Axiomatic semantics is an approach based on mathematical logic

Mathematical logic

Mathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...

 to proving the correctness of computer programs. It is closely related to Hoare logic

Hoare logic

Hoare logic is a formal system with a set of logical rules for reasoning rigorously about the correctness of computer programs. It was proposed in 1969 by the British computer scientist and logician C. A. R. Hoare, and subsequently refined by Hoare and other researchers...

.

Axiomatic semantics define the meaning of a command in a program by describing its effect on assertions about the program state. The assertions are logical statements - predicates with variables, where the variables define the state of the program.

See also

• Algebraic semantics
  Algebraic semantics
  An programming language theory, the algebraic semantics of a programming language is a form of axiomatic semantics based on algebraic laws for describing and reasoning about program semantics in a formal manner....
  
   — in terms of algebras
• Denotational semantics
  Denotational semantics
  In computer science, denotational semantics is an approach to formalizing the meanings of programming languages by constructing mathematical objects which describe the meanings of expressions from the languages...
  
    — by translation of the program into another language
• Operational semantics
  Operational semantics
  In computer science, operational semantics is a way to give meaning to computer programs in a mathematically rigorous way. Operational semantics are classified into two categories: structural operational semantics formally describe how the individual steps of a computation take place in a...
  
   — in terms of the state of the computation
• Formal semantics of programming languages
  Formal semantics of programming languages
  In programming language theory, semantics is the field concerned with the rigorous mathematical study of the meaning of programming languages and models of computation...
  
   — overview
• Predicate transformer semantics
  Predicate transformer semantics
  Predicate transformer semantics was introduced by Dijkstra in his seminal paper "Guarded commands, nondeterminacy and formal derivation of programs". They define the semantics of an imperative programming paradigm by assigning to each statement in this language a corresponding predicate...
  
   — describes the meaning of a program fragment as the function transforming a postcondition
  Postcondition
  In computer programming, a postcondition is a condition or predicate that must always be true just after the execution of some section of code or after an operation in a formal specification. Postconditions are sometimes tested using assertions within the code itself...
  
   to the precondition
  Precondition
  In computer programming, a precondition is a condition or predicate that must always be true just prior to the execution of some section of code or before an operation in a formal specification....
  
  needed to establish it.