A deductive language is a computer

programming language A programming language is a system of notation for writing computer programs. Most programming languages are text-based formal languages, but they may also be graphical. They are a kind of computer language. The description of a programming l ...

in which the program is a collection of predicates ('facts') and rules that connect them. Such a language is used to create

knowledge based system 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 ...

s or

expert system In artificial intelligence, an expert system is a computer system emulating the decision-making ability of a human expert. Expert systems are designed to solve complex problems by reasoning through bodies of knowledge, represented mainly as if� ...

s 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 Prolog is a logic programming language associated with artificial intelligence and computational linguistics. Prolog has its roots in first-order logic, a formal logic, and unlike many other programming languages, Prolog is intended primarily a ...

, or its database-query cousin,

Datalog Datalog is a declarative logic programming language. While it is syntactically a subset of Prolog, Datalog generally uses a bottom-up rather than top-down evaluation model. This difference yields significantly different behavior and properties ...

History

As the name implies, deductive languages are rooted in the principles of deductive reasoning; making inferences based upon current knowledge. The first recommendation to use a clausal form of logic for representing computer programs was made by

Cordell Green Cordell Green (born 1941) is an American computer scientist who is the director and chief scientist of the Kestrel Institute. Green received a B.A. and B.S. from Rice University. At Stanford University, he earned an M.S. and then a PhD in 1969. ...

(1969) at Stanford Research Institute (now

SRI International SRI International (SRI) is an American nonprofit organization, nonprofit scientific research, scientific research institute and organization headquartered in Menlo Park, California. The trustees of Stanford University established SRI in 1946 as ...

). This idea can also be linked back to the battle between procedural and declarative information representation in early artificial intelligence systems. Deductive languages and their use in

logic programming Logic programming is a programming paradigm which is largely based on formal logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of log ...

can also be dated to the same year when Foster and Elcock introduce
Absys
the first deductive/logical programming language. Shortly after, the first Prolog system was introduced in 1972 by Colmerauer through collaboration with

Robert Kowalski Robert Anthony Kowalski (born 15 May 1941) is an American-British logician and computer scientist, whose research is concerned with developing both human-oriented models of computing and computational models of human thinking. He has spent m ...

Components

The components of a deductive language are a system of

formal logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or of logical truths. It is a formal science investigating how conclusions follow from premise ...

and a

knowledge base A knowledge base (KB) is a technology used to store complex structured and unstructured information used by a computer system. The initial use of the term was in connection with expert systems, which were the first knowledge-based systems. ...

upon which the logic is applied.

Formal Logic

Formal logic is the study of inference in regards to formal content. The distinguishing feature between formal and informal logic is that in the former case, the logical rule applied to the content is not specific to a situation. The laws hold regardless of a change in context. Although

first-order logic 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 quanti ...

is described in the example below to demonstrate the uses of a deductive language, no formal system is mandated and the use of a specific system is defined within the language rules or grammar. As input, a predicate takes any object(s) in the domain of interest and outputs either one of two Boolean values: true or false. For example, consider the sentences "Barack Obama is the 44th president" and "If it rains today, I will bring an umbrella". The first is a statement with an associated truth value. The second is a conditional statement relying on the value of some other statement. Either of these sentences can be broken down into predicates which can be compared and form the knowledge base of a deductive language. Moreover, variables such as 'Barack Obama' or 'president' can be quantified over. For example, take 'Barack Obama' as variable 'x'. In the sentence "There exists an 'x' such that if 'x' is the president, then 'x' is the commander in chief." This is an example of the existential quantifier in first order logic. Take 'president' to be the variable 'y'. In the sentence "For every 'y', 'y' is the leader of their nation." This is an example of the universal quantifier.

Knowledge Base

A collection of 'facts' or predicates and variables form the knowledge base of a deductive language. Depending on the language, the order of declaration of these predicates within the knowledge base may or may not influence the result of applying logical rules. Upon application of certain 'rules' or inferences, new predicates may be added to a knowledge base. As new facts are established or added, they form the basis for new inferences. As the core of early expert systems, artificial intelligence systems which can make decisions like an expert human, knowledge bases provided more information than databases. They contained structured data, with classes, subclasses, and instances.

Prolog

is an example of a deductive, declarative language that applies first- order logic to a knowledge base. To run a program in Prolog, a query is posed and based upon the

inference engine In the field of artificial intelligence, an inference engine is a component of the 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 ...

and the specific facts in the knowledge base, a result is returned. The result can be anything appropriate from a new relation or predicate, to a literal such as a Boolean (true/false), depending on the engine and

type system In computer programming, a type system is a logical system comprising a set of rules that assigns a property called a type to every "term" (a word, phrase, or other set of symbols). Usually the terms are various constructs of a computer progra ...

References

* J.M. Foster and E.W. Elcock. ABSYS 1: An Incremental Compiler for Assertions: an Introduction, Machine Intelligence 4, Edinburgh U Press, 1969, pp. 423–429 * Cordell Green. '
Application of Theorem Proving to Problem Solving
'' IJCAI 1969. * Cordell Green
Alumnus of SRI International's Artificial Intelligence Center
retrieved 12/09/14. * Robert Kowalski and Donald and Kuehner
Linear Resolution with Selection Function
Artificial Intelligence, Vol. 2, 1971, pp. 227–60. * Robert Kowalsk
Predicate Logic as a Programming Language
Memo 70, Department of Artificial Intelligence, Edinburgh University. 1973. Also in P {{DEFAULTSORT:Deductive Language Programming languages Computer programming Databases