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Term Indexing
In computer science, a term index is a data structure to facilitate fast lookup of terms and Clause (logic), clauses in a logic programming, logic program, deductive database, or automated theorem prover. Overview Many operations in automatic theorem provers require search in huge collections of terms and clauses. Such operations typically fall into the following scheme. Given a collection S of terms (clauses) and a query term (clause) q, find in S some/all terms t related to q according to a certain retrieval condition. Most interesting retrieval conditions are formulated as existence of a substitution that relates in a special way the query and the retrieved objects t. Here is a list of retrieval conditions frequently used in provers: * term q is unifiable with term t, i.e., there exists a substitution \theta , such that q\theta = t\theta * term t is an instance of q, i.e., there exists a substitution \theta, such that q\theta = t * term t is a generalisation of q, i.e., there ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, applied disciplines (including the design and implementation of Computer architecture, hardware and Software engineering, software). Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of computational problem, problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and preventing security vulnerabilities. Computer graphics (computer science), Computer graphics and computational geometry address the generation of images. Programming language theory considers different ways to describe computational processes, and database theory concerns the management of re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clause (logic)
In logic, a clause is a propositional formula formed from a finite collection of literals (atoms or their negations) and logical connectives. A clause is true either whenever at least one of the literals that form it is true (a disjunctive clause, the most common use of the term), or when all of the literals that form it are true (a conjunctive clause, a less common use of the term). That is, it is a finite disjunction or conjunction of literals, depending on the context. Clauses are usually written as follows, where the symbols l_i are literals: :l_1 \vee \cdots \vee l_n Empty clauses A clause can be empty (defined from an empty set of literals). The empty clause is denoted by various symbols such as \empty, \bot, or \Box. The truth evaluation of an empty disjunctive clause is always false. This is justified by considering that false is the neutral element of the monoid (\, \vee). The truth evaluation of an empty conjunctive clause is always true. This is related to the conc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Logic Programming
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'': :A :- B1, ..., Bn. and are read as declarative sentences in logical form: :A if B1 and ... and Bn. A is called the ''head'' of the rule, B1, ..., Bn is called the ''body'', and the Bi are called '' literals'' or conditions. When n = 0, the rule is called a ''fact'' and is written in the simplified form: :A. Queries (or goals) have the same syntax as the bodies of rules and are commonly written in the form: :?- B1, ..., Bn. In the simplest case of Horn clauses (or "definite" clauses), all ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Deductive Database
A deductive database is a database system that can make deductions (i.e. conclude additional facts) based on rules and facts stored in its database. Datalog is the language typically used to specify facts, rules and queries in deductive databases. Deductive databases have grown out of the desire to combine logic programming with relational databases to construct systems that support a powerful formalism and are still fast and able to deal with very large datasets. Deductive databases are more expressive than relational databases but less expressive than logic programming systems such as Prolog. In recent years, deductive databases have found new application in data integration, information extraction, networking, program analysis, security, and cloud computing. Deductive databases reuse many concepts from logic programming; rules and facts specified in Datalog look very similar to those written in Prolog, but there are some important differences: * Order sensitivity and proced ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Automated Theorem Prover
Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs. Automated reasoning over mathematical proof was a major motivating factor for the development of computer science. Logical foundations While the roots of formalized logic go back to Aristotle, the end of the 19th and early 20th centuries saw the development of modern logic and formalized mathematics. Frege's ''Begriffsschrift'' (1879) introduced both a complete propositional calculus and what is essentially modern predicate logic. His '' Foundations of Arithmetic'', published in 1884, expressed (parts of) mathematics in formal logic. This approach was continued by Russell and Whitehead in their influential ''Principia Mathematica'', first published 1910–1913, and with a revised second edition in 1927. Russell and Whitehead thought they could derive all mathematical truth using axioms ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theta-subsumption
Theta-subsumption (θ-subsumption, or just subsumption) is a decidable relation between two first-order clauses that guarantees that one clause logically entails the other. It was first introduced by John Alan Robinson in 1965 and has become a fundamental notion in inductive logic programming. Deciding whether a given clause θ-subsumes another is an NP-complete problem. Definition A clause, that is, a disjunction of first-order literals, can be considered as a set containing all its disjuncts. With this convention, a clause c_1 θ-subsumes a clause c_2 if there is a substitution \theta such that the clause obtained by applying \theta to c_1 is a subset of c_2. Properties θ-subsumption is a weaker relation than logical entailment, that is, whenever a clause c_1 θ-subsumes a clause c_2, then c_1 logically entails c_2 . However, the converse is not true: A clause can logically entail another clause, but not θ-subsume it. θ-subsumption is decidable; more precisely, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrimination Tree
Discrimination is the process of making unfair or prejudicial distinctions between people based on the groups, classes, or other categories to which they belong or are perceived to belong, such as race, gender, age, class, religion, or sexual orientation. Discrimination typically leads to groups being unfairly treated on the basis of perceived statuses based on ethnic, racial, gender or religious categories. It involves depriving members of one group of opportunities or privileges that are available to members of another group. Discriminatory traditions, policies, ideas, practices and laws exist in many countries and institutions in all parts of the world, including some, where such discrimination is generally decried. In some places, countervailing measures such as quotas have been used to redress the balance in favor of those who are believed to be current or past victims of discrimination. These attempts have often been met with controversy, and sometimes been called reve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Substitution Tree
Substitution may refer to: Arts and media *Substitution (poetry), a variation in poetic scansion * Substitution (theatre), an acting methodology Music *Chord substitution, swapping one chord for a related one within a chord progression *Tritone substitution, reinterpreting a chord via a new root note located an augmented fourth or diminished fifth distant from the root of the original interpretation * "Substitution" (Silversun Pickups song), a 2009 song by Silversun Pickups * "Substitution" (Purple Disco Machine and Kungs song), a 2023 song by Purple Disco Machine and Kungs Science and mathematics Biology and chemistry * Base-pair substitution or point mutation, a type of mutation *Substitution reaction, where a functional group in a chemical compound is replaced by another group **Substituent, the atom or atoms that replaces those of the reactant *Substitution, a process in which an allele arises and undergoes fixation Mathematics and computing *Substitution (algebra), repla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Path Indexing
A path is a route for physical travel – see Trail. Path or PATH may also refer to: Physical paths of different types * Bicycle path * Bridle path, used by people on horseback * Course (navigation), the intended path of a vehicle * Desire path, created by human or animal foot traffic * Footpath, intended for use only by pedestrians * Shared-use path, intended for multiple modes such as walking, bicycling, in-line skating or others * Sidewalk, a paved path along the side of a road * Hoggin, a buff-coloured gravel & clay pathway often seen in gardens of Stately Homes, Parks etc. * Trail, an unpaved lane or road Mathematics, physics, and computing * Path (computing), in file systems, the human-readable address of a resource ** PATH (variable), in computing, a way to specify a list of directories containing executable programs * Path (graph theory), a sequence of edges of a graph ** st-connectivity problem, sometimes known as the "path problem" * Path (topology), a continuous ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trie
In computer science, a trie (, ), also known as a digital tree or prefix tree, is a specialized search tree data structure used to store and retrieve strings from a dictionary or set. Unlike a binary search tree, nodes in a trie do not store their associated key. Instead, each node's ''position'' within the trie determines its associated key, with the connections between nodes defined by individual Character (computing), characters rather than the entire key. Tries are particularly effective for tasks such as autocomplete, spell checking, and IP routing, offering advantages over hash tables due to their prefix-based organization and lack of hash collisions. Every child node shares a common prefix (computer science), prefix with its parent node, and the root node represents the empty string. While basic trie implementations can be memory-intensive, various optimization techniques such as compression and bitwise representations have been developed to improve their efficiency. A n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Handbook Of Automated Reasoning
The ''Handbook of Automated Reasoning'' (, 2128 pages) is a collection of survey articles on the field of automated reasoning. Published in June 2001 by MIT Press, it is edited by John Alan Robinson and Andrei Voronkov. Volume 1 describes methods for classical logic, first-order logic with equality and other theories, and induction. Volume 2 covers higher-order, non-classical and other kinds of logic. Index Volume 1 ;History ;Classical Logic ;Equality and Other Theories ;Induction Volume 2 ;Higher-Order Logic and Logical Frameworks ;Nonclassical Logics ;Decidable Classes and Model Building ;Implementation {{Ordered list , start=26 , I.V. Ramakrishnan, R.Sekar, Andrei Voronkov Andrei Anatolievič Voronkov (born 1959) is a Professor of Formal methods in the Department of Computer Science, University of Manchester, Department of Computer Science at the University of Manchester. Education Voronkov was educated at Novosibir .... Term Indexing, pp. 1853–1964. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
