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First-order logic —also called predicate logic, predicate calculus, quantificational logic —is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables, so that rather than ...
Definition. Logical reasoning is a form of thinking that is concerned with arriving at a conclusion in a rigorous way. [1] This happens in the form of inferences by transforming the information present in a set of premises to reach a conclusion. [2] [3] It can be defined as "selecting and interpreting information from a given context, making ...
A form of argument involving two conditional statements and their negated consequents, leading to the negation of at least one of the antecedents. determiner. A word, phrase, or affix that specifies the reference of a noun or noun phrase, such as "the", "some", "every". deterministic polynomial time.
Logic plays a fundamental role in computer science. Some of the key areas of logic that are particularly significant are computability theory (formerly called recursion theory), modal logic and category theory. The theory of computation is based on concepts defined by logicians and mathematicians such as Alonzo Church and Alan Turing.
In logic, the logical form of a statement is a precisely-specified semantic version of that statement in a formal system. Informally, the logical form attempts to formalize a possibly ambiguous statement into a statement with a precise, unambiguous logical interpretation with respect to a formal system. In an ideal formal language, the meaning ...
Logical constant. In logic, a logical constant or constant symbol of a language is a symbol that has the same semantic value under every interpretation of . Two important types of logical constants are logical connectives and quantifiers. The equality predicate (usually written '=') is also treated as a logical constant in many systems of logic .
In mathematical logic, a first-order predicate is a predicate that takes only individual (s) constants or variables as argument (s). [1] Compare second-order predicate and higher-order predicate . This is not to be confused with a one-place predicate or monad, which is a predicate that takes only one argument. For example, the expression "is a ...
Philosophical logic. Understood in a narrow sense, philosophical logic is the area of logic that studies the application of logical methods to philosophical problems, often in the form of extended logical systems like modal logic. Some theorists conceive philosophical logic in a wider sense as the study of the scope and nature of logic in general.