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SLD Resolution
SLD resolution (''Selective Linear Definite'' clause resolution) is the basic inference rule used in logic programming. It is a refinement of resolution, which is both sound and refutation complete for Horn clauses. The SLD inference rule Given a goal clause, represented as the negation of a problem to be solved : \neg L_1 \lor \cdots \lor \neg L_i \lor \cdots \lor \neg L_n with selected literal \neg L_i , and an input definite clause: L \lor \neg K_1 \lor \cdots \lor \neg K_m whose positive literal (atom) L\, unifies with the atom L_i \, of the selected literal \neg L_i \, , SLD resolution derives another goal clause, in which the selected literal is replaced by the negative literals of the input clause and the unifying substitution \theta \, is applied: (\neg L_1 \lor \cdots \lor \neg K_1 \lor \cdots \lor \neg K_m\ \lor \cdots \lor \neg L_n)\theta In the simplest case, in propositional logic, the atoms L_i \, and L \, are identical, and the unifying ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rule Of Inference
In the philosophy of logic, 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 (or conclusions). 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 (as well as the semantics of many other non-classical logics), in the sense that if the premises are true (under an interpretation), then so is the conclusion. Typically, a rule of inference preserves truth, a semantic property. In many-valued logic, it preserves a general designation. But a rule of inference's action is purely syntactic, and does not need to preserve any semantic property: any function from sets of formulae to formulae counts as a rule of inference. Usually only rules that are recursive are important; i.e. r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Search Tree
In computer science, a search tree is a tree data structure used for locating specific keys from within a set. In order for a tree to function as a search tree, the key for each node must be greater than any keys in subtrees on the left, and less than any keys in subtrees on the right. The advantage of search trees is their efficient search time given the tree is reasonably balanced, which is to say the leaves at either end are of comparable depths. Various search-tree data structures exist, several of which also allow efficient insertion and deletion of elements, which operations then have to maintain tree balance. Search trees are often used to implement an associative array. The search tree algorithm uses the key from the key–value pair to find a location, and then the application stores the entire key–value pair at that particular location. Types of Trees Binary search tree A Binary Search Tree is a node-based data structure where each node contains a key and two s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jean Gallier
Jean Henri Gallier (born 1949) is a researcher in computational logic at the University of Pennsylvania, where he holds appointments in the Computer and Information Science Department and the Department of Mathematics. Biography Gallier was born January 5, 1949, in Nancy, France, and holds dual French and American citizenship. He earned his baccalauréat at the Lycée de Sèvres in 1966, and a degree in civil engineering at the École Nationale des Ponts et Chaussées in 1972. He then moved to the University of California, Los Angeles for his graduate studies, earning a Ph.D. in computer science in 1978 under the joint supervision of Sheila Greibach and Emily Perlinski Friedman. His dissertation was entitled ''Semantics and Correctness of Classes of Deterministic and Nondeterministic Recursive Programs''. After postdoctoral study at the University of California, Santa Barbara, he joined the University of Pennsylvania Department of Computer and Information Science in 1978. At Pennsy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Alan Robinson
John Alan Robinson (9 March 1930 – 5 August 2016) was a philosopher, mathematician, and computer scientist. He was a professor emeritus at Syracuse University. Alan Robinson's major contribution is to the foundations of automated theorem proving. His unification algorithm eliminated one source of combinatorial explosion in resolution provers; it also prepared the ground for the logic programming paradigm, in particular for the Prolog language. Robinson received the 1996 Herbrand Award for Distinguished Contributions to Automated reasoning. Life Robinson was born in Halifax, Yorkshire, England in 1930 and left for the United States in 1952 with a classics degree from Cambridge University. He studied philosophy at the University of Oregon before moving to Princeton University where he received his PhD in philosophy in 1956. He then worked at Du Pont as an operations research analyst, where he learned programming and taught himself mathematics. He moved to Rice Universit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Negation As Failure
Negation as failure (NAF, for short) is a non-monotonic inference rule in logic programming, used to derive \mathrm~p (i.e. that ~p is assumed not to hold) from failure to derive ~p. Note that \mathrm ~p can be different from the statement \neg p of the logical negation of ~p, depending on the completeness of the inference algorithm and thus also on the formal logic system. Negation as failure has been an important feature of logic programming since the earliest days of both Planner and Prolog. In Prolog, it is usually implemented using Prolog's extralogical constructs. More generally, this kind of negation is known as weak negation, in contrast with the strong (i.e. explicit, provable) negation. Planner semantics In Planner, negation as failure could be implemented as follows: :''if'' (''not'' (''goal'' p)), ''then'' (''assert'' ¬p) which says that if an exhaustive search to prove p fails, then assert ¬p. This states that proposition p shall be assumed as "not true" in an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Krzysztof R
Krzysztof () is a Polish given name, equivalent to English '' Christopher''. The name became popular in the 15th century. Its diminutive forms include Krzyś, Krzysiek, and Krzysio; augmentative – Krzychu Individuals named Krzysztof may choose to celebrate their name day on March 15, July 25, March 2, May 21, August 20 or October 31. People with the first name Krzysztof * Krzysztof Arciszewski (1592–1656), Polish military man * Krzysztof Bednarski (born 1953), famous contemporary Polish sculptor * Krzysztof Bizacki (born 1973), Polish footballer * Krzysztof Bukalski (born 1970), Polish footballer * Krzysztof Charamsa (born 1972), Polish priest * Krzysztof Chodkiewicz, d. 1652, Polish-Lithuanian nobleman * Krzysztof Cwalina (born 1971), Polish freestyle swimmer * Krzysztof Czerwinski (Krzysztof Czerwiński) (born 1980), Polish conductor, organist and voice teacher * Krzysztof Dabrowski (Krzysztof Dąbrowski) (born 1978), Polish footballer * Krzysztof Głowacki (born 1 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Branch-and-bound
Branch and bound (BB, B&B, or BnB) is an algorithm design paradigm for discrete and combinatorial optimization problems, as well as mathematical optimization. A branch-and-bound algorithm consists of a systematic enumeration of candidate solutions by means of state space search: the set of candidate solutions is thought of as forming a rooted tree with the full set at the root. The algorithm explores ''branches'' of this tree, which represent subsets of the solution set. Before enumerating the candidate solutions of a branch, the branch is checked against upper and lower estimated ''bounds'' on the optimal solution, and is discarded if it cannot produce a better solution than the best one found so far by the algorithm. The algorithm depends on efficient estimation of the lower and upper bounds of regions/branches of the search space. If no bounds are available, the algorithm degenerates to an exhaustive search. The method was first proposed by Ailsa Land and Alison Doig whils ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Best-first Search
Best-first search is a class of search algorithms, which explore a graph by expanding the most promising node chosen according to a specified rule. Judea Pearl described the best-first search as estimating the promise of node ''n'' by a "heuristic evaluation function f(n) which, in general, may depend on the description of ''n'', the description of the goal, the information gathered by the search up to that point, and most importantly, on any extra knowledge about the problem domain.". pp. 94 and 95 (note 3). Some authors have used "best-first search" to refer specifically to a search with a heuristic that attempts to predict how close the end of a path is to a solution (or, goal), so that paths which are judged to be closer to a solution (or, goal) are extended first. This specific type of search is called '' greedy best-first search'' or ''pure heuristic search''. Efficient selection of the current best candidate for extension is typically implemented using a priority queue. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Breadth-first Search
Breadth-first search (BFS) is an algorithm for searching a tree data structure for a node that satisfies a given property. It starts at the tree root and explores all nodes at the present depth prior to moving on to the nodes at the next depth level. Extra memory, usually a queue, is needed to keep track of the child nodes that were encountered but not yet explored. For example, in a chess endgame a chess engine may build the game tree from the current position by applying all possible moves, and use breadth-first search to find a win position for white. Implicit trees (such as game trees or other problem-solving trees) may be of infinite size; breadth-first search is guaranteed to find a solution node if one exists. In contrast, (plain) depth-first search, which explores the node branch as far as possible before backtracking and expanding other nodes, may get lost in an infinite branch and never make it to the solution node. Iterative deepening depth-first search avoid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Depth-first Search
Depth-first search (DFS) is an algorithm for traversing or searching tree or graph data structures. The algorithm starts at the root node (selecting some arbitrary node as the root node in the case of a graph) and explores as far as possible along each branch before backtracking. Extra memory, usually a stack, is needed to keep track of the nodes discovered so far along a specified branch which helps in backtracking of the graph. A version of depth-first search was investigated in the 19th century by French mathematician Charles Pierre Trémaux as a strategy for solving mazes. Properties The time and space analysis of DFS differs according to its application area. In theoretical computer science, DFS is typically used to traverse an entire graph, and takes time where , V, is the number of vertices and , E, the number of edges. This is linear in the size of the graph. In these applications it also uses space O(, V, ) in the worst case to store the stack of vertices on t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Backward Reasoning
Backward chaining (or backward reasoning) 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 game theory, researchers apply it to (simpler) subgames to find a solution to the game, in a process called ''backward induction''. In chess, it is called retrograde analysis, and it is used to generate table bases for chess endgames for computer chess. Backward chaining is implemented in logic programming by SLD resolution. Both rules are based on the modus ponens inference rule. It is one of the two most commonly used methods of reasoning with inference rules and logical implications – the other is forward chaining. Backward chaining systems usually employ a depth-first search strategy, e.g. Prolog. How it works Backward chaining starts with a list of goals (or a hypothesis) and works backwards from the consequent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
