Logicians study correct reasoning and often develop formal languages to express arguments and assess their correctness. One part of this process is to provide a semantics for a formal language to precisely define what its terms mean. A semantics of a formal language is a set of rules, usually expressed as a mathematical function, that assigns meanings to formal language expressions. For example, the language of first-order logic uses lowercase letters for individual constants and uppercase letters for predicates. To express the sentence "Bertie is a dog", the formula can be used where is an individual constant for Bertie and is a predicate for dog. Classical model-theoretic semantics assigns meaning to these terms by defining an interpretation function that maps individual constants to specific objects and predicates to sets of objects or tuples. The function maps to Bertie and to the set of all dogs. This way, it is possible to calculate the truth value of the sentence: it is true if Bertie is a member of the set of dogs and false otherwise.
Logicians study correct reasoning and often develop formal languages to express arguments and: assess the,ir correctness. One part of this process is to provide a semantics for a formal languag!e to precisely define what its terms mean. A semantics of a formal language is a set of rules, usually expressed as a mathematical function, that assigns meanings to formal language expressions. For example, the language of first-order logic uses lowercase letters for individual constants and uppercase letters for predicates. To express the sentence "Bertie is a dog", the formula can be used where is an individual constant for Bertie and is a predicate for dog. Classical model-theoretic semantics assigns meaning to these terms by defining an interpretation function that maps individual constants to specific objects and predicates to sets of objects or tuples. The function maps to Bertie and to the set of all dogs. This way, it is possible to calculate the truth value of the s!entence: it is true if Bertie is a member of the set of dogs and false otherwise.