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Contraposition. In logic and mathematics, contraposition, or transposition, refers to the inference of going from a conditional statement into its logically equivalent contrapositive, and an associated proof method known as § Proof by contrapositive. The contrapositive of a statement has its antecedent and consequent inverted and flipped.
Jape (software) Jape is a configurable, graphical proof assistant, originally developed by Richard Bornat at Queen Mary, University of London and Bernard Sufrin the University of Oxford. [2] The program is available for the Mac, Unix, and Windows operating systems. It is written in the Java programming language and released under the GNU GPL.
Linear temporal logic. In logic, linear temporal logic or linear-time temporal logic[1][2] (LTL) is a modal temporal logic with modalities referring to time. In LTL, one can encode formulae about the future of paths, e.g., a condition will eventually be true, a condition will be true until another fact becomes true, etc.
The release on December 8, 1998 and subsequent releases through J2SE 5.0 were rebranded retrospectively Java 2 and the version name "J2SE" (Java 2 Platform, Standard Edition) replaced JDK to distinguish the base platform from J2EE (Java 2 Platform, Enterprise Edition) and J2ME (Java 2 Platform, Micro Edition). This was a very significant ...
The classic proof that the square root of 2 is irrational is a refutation by contradiction. [11] Indeed, we set out to prove the negation ¬ ∃ a, b ∈ . a/b = √ 2 by assuming that there exist natural numbers a and b whose ratio is the square root of two, and derive a contradiction.
The final release date of the JPA 1.0 specification was 11 May 2006 as part of Java Community Process JSR 220. The JPA 2.0 specification was released 10 December 2009 (the Java EE 6 platform requires JPA 2.0 [2]). The JPA 2.1 specification was released 22 April 2013 (the Java EE 7 platform requires JPA 2.1 [3]). The JPA 2.2 specification was ...
A propositional proof system Pp-simulatesQ (written as P ≤ pQ) when there is a polynomial-time function F such that P (F (x)) = Q (x) for every x. 1 That is, given a Q -proof x, we can find in polynomial time a P -proof of the same tautology. If P ≤ pQ and Q ≤ pP, the proof systems P and Q are p-equivalent.
Proof complexity. In logic and theoretical computer science, and specifically proof theory and computational complexity theory, proof complexity is the field aiming to understand and analyse the computational resources that are required to prove or refute statements. Research in proof complexity is predominantly concerned with proving proof ...