A rule of inference, inference rule or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion. For example, the rule of inference called modus ponens takes two premises, one in the form "If p then q" and another in the form "p", and returns the conclusion "q". The rule is valid with respect to the semantics of classical logic, in the sense that if the premises are true, then so is the conclusion.
Deep structure and surface structure concepts are used in linguistics, specifically in the study of syntax in the Chomskyan tradition of transformational generative grammar.
In mathematics, computer science, and logic, rewriting covers a wide range of methods of replacing subterms of a formula with other terms. The objects of focus for this article include rewriting systems. In their most basic form, they consist of a set of objects, plus relations on how to transform those objects.
The Knuth–Bendix completion algorithm is a semi-decision algorithm for transforming a set of equations into a confluent term rewriting system. When the algorithm succeeds, it effectively solves the word problem for the specified algebra.
The Maude system is an implementation of rewriting logic developed at SRI International. It is similar in its general approach to Joseph Goguen's OBJ3 implementation of equational logic, but based on rewriting logic rather than order-sorted equational logic, and with a heavy emphasis on powerful metaprogramming based on reflection.
In computer science, graph transformation, or graph rewriting, concerns the technique of creating a new graph out of an original graph algorithmically. It has numerous applications, ranging from software engineering to layout algorithms and picture generation.
A knowledge-based system (KBS) is a computer program that reasons and uses a knowledge base to solve complex problems. The term is broad and refers to many different kinds of systems. The one common theme that unites all knowledge based systems is an attempt to represent knowledge explicitly and a reasoning system that allows it to derive new knowledge. Thus, a knowledge-based system has two distinguishing features: a knowledge base and an inference engine.
Constraint Handling Rules (CHR) is a declarative, rule-based language, introduced in 1991 by Thom Frühwirth at the time with ECRC in Munich, Germany. Originally intended for constraint programming, CHR finds applications in grammar induction, abductive reasoning, multi-agent systems, natural language processing, compilation, scheduling, spatial-temporal reasoning, testing and verification, and type systems.
A production system is a computer program typically used to provide some form of artificial intelligence, which consists primarily of a set of rules about behavior but it also includes the mechanism necessary to follow those rules as the system responds to states of the world. Those rules, termed productions, are a basic representation found useful in automated planning, expert systems and action selection.
In philosophy, a formal fallacy, deductive fallacy, logical fallacy or non sequitur is a pattern of reasoning rendered invalid by a flaw in its logical structure that can neatly be expressed in a standard logic system, for example propositional logic. It is defined as a deductive argument that is invalid. The argument itself could have true premises, but still have a false conclusion. Thus, a formal fallacy is a fallacy where deduction goes wrong, and is no longer a logical process. This may not affect the truth of the conclusion, since validity and truth are separate in formal logic.
In computer science, confluence is a property of rewriting systems, describing which terms in such a system can be rewritten in more than one way, to yield the same result. This article describes the properties in the most abstract setting of an abstract rewriting system.
In abstract rewriting, an object is in normal form if it cannot be rewritten any further. Depending on the rewriting system and the object, several normal forms may exist, or none at all.
Orthogonality as a property of term rewriting systems describes where the reduction rules of the system are all left-linear, that is each variable occurs only once on the left hand side of each reduction rule, and there is no overlap between them.
In mathematics, in the theory of rewriting systems, Newman's lemma, also commonly called the diamond lemma, states that a terminating abstract rewriting system (ARS), that is, one in which there are no infinite reduction sequences, is confluent if it is locally confluent. In fact a terminating ARS is confluent precisely when it is locally confluent.
In computer science, termination analysis is program analysis which attempts to determine whether the evaluation of a given program halts for each input. This means to determine whether the input program computes a total function.
A premise or premiss is a statement that an argument claims will induce or justify a conclusion. It is an assumption that something is true.
In computer science, a computation is said to diverge if it does not terminate or terminates in an exceptional state. Otherwise it is said to converge. In domains where computations are expected to be infinite, such as process calculi, a computation is said to diverge if it fails to be productive.
In mathematical logic and theoretical computer science, an abstract rewriting system is a formalism that captures the quintessential notion and properties of rewriting systems. In its simplest form, an ARS is simply a set together with a binary relation, traditionally denoted with ; this definition can be further refined if we index (label) subsets of the binary relation. Despite its simplicity, an ARS is sufficient to describe important properties of rewriting systems like normal forms, termination, and various notions of confluence.
In mathematical logic, a critical pair arises in term rewriting systems where rewrite rules overlap to yield two different terms. In more detail, is a critical pair if there is a term t for which two different applications of a rewrite rule yield the terms t1 and t2.
