Search results
Results from the WOW.Com Content Network
Syntax is usually associated with the rules (or grammar) governing the composition of texts in a formal language that constitute the well-formed formulas of a formal system. In computer science, the term syntax refers to the rules governing the composition of well-formed expressions in a programming language. As in mathematical logic, it is ...
Syntactic accounts of logical consequence rely on schemes using inference rules. For instance, we can express the logical form of a valid argument as: All X are Y All Y are Z Therefore, all X are Z. This argument is formally valid, because every instance of arguments constructed using this scheme is valid.
Logical grammar or rational grammar is a term used in the history and philosophy of linguistics to refer to certain linguistic and grammatical theories that were prominent until the early 19th century and later influenced 20th-century linguistic thought.
Philosophy of logic is the area of philosophy that studies the nature of logic. [1] [2] Like many other disciplines, logic involves various philosophical presuppositions which are addressed by the philosophy of logic. [3]
The approach applies the mathematical techniques of model theory to the task of syntactic description: a grammar is a theory in the logician's sense (a consistent set of statements) and the well-formed structures are the models that satisfy the theory.
In the philosophy of logic and logic, specifically in deductive reasoning, a rule of inference, inference rule or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion (or conclusions).
The theorem is a syntactic consequence of all the well-formed formulas preceding it in the proof. For a well-formed formula to qualify as part of a proof, it must be the result of applying a rule of the deductive apparatus (of some formal system) to the previous well-formed formulas in the proof sequence.
Gerhard Gentzen, Dag Prawitz and Michael Dummett are generally seen as the founders of this approach; it is heavily influenced by Ludwig Wittgenstein's later philosophy, especially his aphorism "meaning is use".