Language, Proof and Logic is an educational software package, devised and written by Jon Barwise and John Etchemendy, geared to teaching formal logic...

logic and mathematics, a formal proof or derivation is a finite sequence of sentences (known as well-formed formulas when relating to formal language)...

mathematical literature, proofs are written in terms of rigorous informal logic. Purely formal proofs, written fully in symbolic language without the involvement...

Proof theory is a major branch of mathematical logic and theoretical computer science within which proofs are treated as formal mathematical objects,...

proving in first-order logic. First-order logic also satisfies several metalogical theorems that make it amenable to analysis in proof theory, such as the...

Language, Truth and Logic is a 1936 book about meaning by the philosopher Alfred Jules Ayer, in which the author defines, explains, and argues for the...

Propositional logic is a branch of logic. It is also called statement logic, sentential calculus, propositional calculus, sentential logic, or sometimes...

the steps in the proof and all the important ideas faithfully, while restating the proof in the modern language of mathematical logic. This outline should...

science and mathematical logic, a proof assistant or interactive theorem prover is a software tool to assist with the development of formal proofs by human–machine...

Press of America, 1998, p. 48. Barwise, Jon; Etchemendy, John. Language, Proof and Logic (1999): 42. Beer, Francis A. "Validities: A Political Science...

Constructive logic is a family of logics where proofs must be constructive (i.e., proving something means one must build or exhibit it, not just argue...

is such a theory, and φ is a sentence (in the same language) and every model of T is a model of φ, then there is a (first-order) proof of φ using the statements...

resource-boundedness, duality, and interaction. Linear logic lends itself to many different presentations, explanations, and intuitions. Proof-theoretically, it derives...

logic is a branch of metamathematics that studies formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and...

mathematical logic, a proof calculus or a proof system is built to prove statements. A proof system includes the components: Formal language: The set L...

In logic and proof theory, natural deduction is a kind of proof calculus in which logical reasoning is expressed by inference rules closely related to...

Quantifiers in Language and Logic. Clarendon Press. pp. 34–. ISBN 978-0-19-929125-0. Barwise, Jon; and Etchemendy, John, 2000. Language Proof and Logic. CSLI (University...

Classical logic Computability logic Deontic logic Dependence logic Description logic Deviant logic Doxastic logic Epistemic logic First-order logic Formal...

An infinitary logic is a logic that allows infinitely long statements and/or infinitely long proofs. The concept was introduced by Zermelo in the 1930s...

between logic and metalogic. While logic deals with proofs in a formal system, expressed in some formal language, metalogic deals with proofs about a...

In logic, the semantics of logic or formal semantics is the study of the meaning and interpretation of formal languages, formal systems, and (idealizations...

widely used object logic is Isabelle/HOL, although significant set theory developments were completed in Isabelle/ZF. Isabelle's main proof method is a higher-order...

Neumann (1927) and Herbrand (1931). Stronger logics, such as second-order logic, are not complete. A consistency proof is a mathematical proof that a particular...

In 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...

have been instantiated. In formal logic, proofs can be represented by sequences of formulas with certain properties, and the final formula in the sequence...

foundation of logic of computable functions previously proposed by Dana Scott. Work on the LCF system introduced the general-purpose programming language ML to...

articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics. Logic studies arguments...

mathematical logic and in the philosophy of mathematics. The theorems are interpreted as showing that Hilbert's program to find a complete and consistent...

Minsky and Seymour Papert. Although it was based on the proof methods of logic, Planner, developed by Carl Hewitt at MIT, was the first language to emerge...

the notion of constructive proof. In particular, systems of intuitionistic logic do not assume the law of excluded middle and double negation elimination...