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The cut, in Prolog, is a goal, written as !
, which always succeeds but cannot be backtracked. Cuts can prevent unwanted backtracking, which could add unwanted solutions and/or space/time overhead to a query.
The cut should be used sparingly. While cuts can be inserted into code containing errors, if a test is unnecessary because a cut has guaranteed that it is true, it is good practice to say so in a comment at the appropriate place. [1]
Some programmers call the cut a controversial control facility [2] because it was added for efficiency reasons only and is not a logical formula.
The use of a cut that only improves efficiency is referred to as a green cut. Green cuts are used to make programs more efficient without changing program output. For example:
gamble(X):-gotmoney(X),!.gamble(X):-gotcredit(X),\+gotmoney(X).
This is called a greencut operator. The ! tells the interpreter to stop looking for alternatives; however, if gotmoney(X)
fails it will check the second rule. Although checking for gotmoney(X)
in the second rule may appear redundant since Prolog's appearance is dependent on gotmoney(X)
failing before, otherwise the second rule would not be evaluated in the first place. Adding \+ gotmoney(X)
guarantees that the second rule will always work, even if the first rule is removed by accident, changed, or moved after the second one.
A cut that is not a green cut is referred to as a red cut, for example:
gamble(X):-gotmoney(X),!.gamble(X):-gotcredit(X).
Proper placement of the cut operator and the order of the rules are required to determine their logical meaning. If for any reason the first rule is removed (e.g. by a cut-and-paste accident) or moved after the second one, the second rule will be broken, i.e., it will not guarantee the rule \+ gotmoney(X)
.
First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—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 propositions such as "Socrates is a man", one can have expressions in the form "there exists x such that x is Socrates and x is a man", where "there exists" is a quantifier, while x is a variable. This distinguishes it from propositional logic, which does not use quantifiers or relations; in this sense, propositional logic is the foundation of first-order logic.
Knowledge representation and reasoning is the field of artificial intelligence (AI) dedicated to representing information about the world in a form that a computer system can use to solve complex tasks such as diagnosing a medical condition or having a dialog in a natural language. Knowledge representation incorporates findings from psychology about how humans solve problems and represent knowledge, in order to design formalisms that will make complex systems easier to design and build. Knowledge representation and reasoning also incorporates findings from logic to automate various kinds of reasoning.
Logic programming is a programming, database and knowledge representation paradigm based on formal logic. A logic program is a set of sentences in logical form, representing knowledge about some problem domain. Computation is performed by applying logical reasoning to that knowledge, to solve problems in the domain. Major logic programming language families include Prolog, Answer Set Programming (ASP) and Datalog. In all of these languages, rules are written in the form of clauses:
Prolog is a logic programming language that has its origins in artificial intelligence, automated theorem proving and computational linguistics.
Planner is a programming language designed by Carl Hewitt at MIT, and first published in 1969. First, subsets such as Micro-Planner and Pico-Planner were implemented, and then essentially the whole language was implemented as Popler by Julian Davies at the University of Edinburgh in the POP-2 programming language. Derivations such as QA4, Conniver, QLISP and Ether were important tools in artificial intelligence research in the 1970s, which influenced commercial developments such as Knowledge Engineering Environment (KEE) and Automated Reasoning Tool (ART).
Inductive logic programming (ILP) is a subfield of symbolic artificial intelligence which uses logic programming as a uniform representation for examples, background knowledge and hypotheses. The term "inductive" here refers to philosophical rather than mathematical induction. Given an encoding of the known background knowledge and a set of examples represented as a logical database of facts, an ILP system will derive a hypothesised logic program which entails all the positive and none of the negative examples.
Constraint programming (CP) is a paradigm for solving combinatorial problems that draws on a wide range of techniques from artificial intelligence, computer science, and operations research. In constraint programming, users declaratively state the constraints on the feasible solutions for a set of decision variables. Constraints differ from the common primitives of imperative programming languages in that they do not specify a step or sequence of steps to execute, but rather the properties of a solution to be found. In addition to constraints, users also need to specify a method to solve these constraints. This typically draws upon standard methods like chronological backtracking and constraint propagation, but may use customized code like a problem-specific branching heuristic.
In computer science, declarative programming is a programming paradigm—a style of building the structure and elements of computer programs—that expresses the logic of a computation without describing its control flow.
In mathematical logic and logic programming, a Horn clause is a logical formula of a particular rule-like form that gives it useful properties for use in logic programming, formal specification, universal algebra and model theory. Horn clauses are named for the logician Alfred Horn, who first pointed out their significance in 1951.
In the field of artificial intelligence, an inference engine is a software component of an intelligent system that applies logical rules to the knowledge base to deduce new information. The first inference engines were components of expert systems. The typical expert system consisted of a knowledge base and an inference engine. The knowledge base stored facts about the world. The inference engine applied logical rules to the knowledge base and deduced new knowledge. This process would iterate as each new fact in the knowledge base could trigger additional rules in the inference engine. Inference engines work primarily in one of two modes either special rule or facts: forward chaining and backward chaining. Forward chaining starts with the known facts and asserts new facts. Backward chaining starts with goals, and works backward to determine what facts must be asserted so that the goals can be achieved.
Backward chaining is an inference method described colloquially as working backward from the goal. It is used in automated theorem provers, inference engines, proof assistants, and other artificial intelligence applications.
In mathematics and computer science, a recursive definition, or inductive definition, is used to define the elements in a set in terms of other elements in the set. Some examples of recursively-definable objects include factorials, natural numbers, Fibonacci numbers, and the Cantor ternary set.
In computer science, the occurs check is a part of algorithms for syntactic unification. It causes unification of a variable V and a structure S to fail if S contains V.
Constraint Handling Rules (CHR) is a declarative, rule-based programming language, introduced in 1991 by Thom Frühwirth at the time with European Computer-Industry Research Centre (ECRC) in Munich, Germany. Originally intended for constraint programming, CHR finds applications in grammar induction, type systems, abductive reasoning, multi-agent systems, natural language processing, compilation, scheduling, spatial-temporal reasoning, testing, and verification.
Twelf is an implementation of the logical framework LF developed by Frank Pfenning and Carsten Schürmann at Carnegie Mellon University. It is used for logic programming and for the formalization of programming language theory.
In computer science, higher-order abstract syntax is a technique for the representation of abstract syntax trees for languages with variable binders.
Constraint logic programming is a form of constraint programming, in which logic programming is extended to include concepts from constraint satisfaction. A constraint logic program is a logic program that contains constraints in the body of clauses. An example of a clause including a constraint is A(X,Y):-X+Y>0,B(X),C(Y)
. In this clause, X+Y>0
is a constraint; A(X,Y)
, B(X)
, and C(Y)
are literals as in regular logic programming. This clause states one condition under which the statement A(X,Y)
holds: X+Y
is greater than zero and both B(X)
and C(Y)
are true.
A deductive language is a computer programming language in which the program is a collection of predicates ('facts') and rules that connect them. Such a language is used to create knowledge based systems or expert systems which can deduce answers to problem sets by applying the rules to the facts they have been given. An example of a deductive language is Prolog, or its database-query cousin, Datalog.
In computer science, a rule-based system is a computer system in which domain-specific knowledge is represented in the form of rules and general-purpose reasoning is used to solve problems in the domain.
The syntax and semantics of Prolog, a programming language, are the sets of rules that define how a Prolog program is written and how it is interpreted, respectively. The rules are laid out in ISO standard ISO/IEC 13211 although there are differences in the Prolog implementations.