First-order logicType of logical systemIn mathematics, philosophy, linguistics, and computer science, first-order logic (FOL), also called predicate logic, predicate calculus, or quantificational logic, is a type of formal system. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables.
Propositional logicPropositional logic is a branch of classical logic. It is also called statement logic, sentential calculus, propositional calculus, sentential logic, or sometimes zeroth-order logic. Sometimes, it is called first-order propositional logic to contrast it with System F, but it is distinct from first-order logic. It deals with propositions (which can be true or false) and relations between propositions, including the construction of arguments based on them.
Mathematical proofA mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference.
Mathematical logicMathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include usage of logic to characterize correct mathematical reasoning or to establish foundations of mathematics.
LogicismIn philosophy of mathematics, logicism is a school of thought comprising one or more of the theses that – for some coherent meaning of 'logic' – mathematics is an extension of logic, some or all of mathematics is reducible to logic, or some or all of mathematics may be modelled in logic. Bertrand Russell and Alfred North Whitehead championed this programme, initiated by Gottlob Frege and subsequently developed by Richard Dedekind and Giuseppe Peano.
Automated reasoningIn computer science, in particular in knowledge representation and reasoning and metalogic, the area of automated reasoning is dedicated to understanding different aspects of reasoning. The study of automated reasoning helps produce computer programs that allow computers to reason completely, or nearly completely, automatically.
Thoralf SkolemThoralf Albert Skolem (Norwegian:; 23 May 1887 – 23 March 1963) was a Norwegian mathematician who worked in mathematical logic, set theory, and number theory. LifeAlthough Skolem's father was a primary school teacher, most of his extended family were farmers. Skolem attended secondary school in Kristiania (later renamed Oslo), passing the university entrance examinations in 1905.
Computer scienceStudy of computationFundamental areas of computer scienceProgramming language theoryComputer architectureArtificial intelligenceComputational complexity theoryComputer science is the study of computation, information, and automation, together with their associated phenomena.
TheoremIn mathematics and formal logic, a theorem is a statement that has been proven, or can be proven. The proof of a theorem is a logical argument that uses the inference rules of a deductive system to establish that the theorem is a logical consequence of the axioms and previously proved theorems.
Computer programA computer program is a sequence or set of instructions in a programming language for a computer to execute. It is one component of software, which also includes documentation and other intangible components. A computer program in its human-readable form is called source code. Source code needs another computer program to execute because computers can only execute their native machine instructions.
Term logicIn logic and formal semantics, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to formal logic that began with Aristotle and was developed further in ancient history mostly by his followers, the Peripatetics. It was revived after the third century CE by Porphyry's Isagoge.Herbrand structureIn first-order logic, a Herbrand structure S {\displaystyle S} is a structure over a vocabulary σ {\displaystyle \sigma } (also sometimes called a signature) that is defined solely by the syntactical properties of σ {\displaystyle \sigma } . The idea is to take the symbol strings of terms as their values, e.g. the denotation of a constant symbol c {\displaystyle c} is just " c {\displaystyle c} " (the symbol). It is named after Jacques Herbrand.*As an Amazon Associate I earn from qualifying purchases.