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In logic and computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY, SAT or B-SAT) is the problem of determining if there exists an interpretation that satisfies a given Boolean formula. In other words, it asks whether the variables of a given Boolean formula can be consistently replaced by the values TRUE or FALSE in such a way that the formula evaluates to TRUE. If this is the case, the formula is called satisfiable. On the other hand, if no such assignment exists, the function expressed by the formula is FALSE for all possible variable assignments and the formula is unsatisfiable. For example, the formula "a AND NOT b" is satisfiable because one can find the values a = TRUE and b = FALSE, which make (a AND NOT b) = TRUE. In contrast, "a AND NOT a" is unsatisfiable.
Loglan is a logical constructed language originally designed for linguistic research, particularly for investigating the Sapir–Whorf hypothesis. The language was developed beginning in 1955 by Dr. James Cooke Brown with the goal of making a language so different from natural languages that people learning it would think in a different way if the hypothesis were true. In 1960, Scientific American published an article introducing the language. Loglan is the first among, and the main inspiration for, the languages known as logical languages, which also includes Lojban.
In mathematics, a finitary relation over a sequence of sets X1, ..., Xn is a subset of the Cartesian product X1 × ... × Xn; that is, it is a set of n-tuples (x1, ..., xn), each being a sequence of elements xi in the corresponding Xi. Typically, the relation describes a possible connection between the elements of an n-tuple. For example, the relation "x is divisible by y and z" consists of the set of 3-tuples such that when substituted to x, y and z, respectively, make the sentence true.
In linguistics, syntax is the study of how words and morphemes combine to form larger units such as phrases and sentences. Central concerns of syntax include word order, grammatical relations, hierarchical sentence structure (constituency), agreement, the nature of crosslinguistic variation, and the relationship between form and meaning (semantics). There are numerous approaches to syntax that differ in their central assumptions and goals.
Combinatory logic is a notation to eliminate the need for quantified variables in mathematical logic. It was introduced by Moses Schönfinkel and Haskell Curry, and has more recently been used in computer science as a theoretical model of computation and also as a basis for the design of functional programming languages. It is based on combinators, which were introduced by Schönfinkel in 1920 with the idea of providing an analogous way to build up functions—and to remove any mention of variables—particularly in predicate logic. A combinator is a higher-order function that uses only function application and earlier defined combinators to define a result from its arguments.
In mathematical logic, a predicate variable is a predicate letter which functions as a "placeholder" for a relation, but which has not been specifically assigned any particular relation. Common symbols for denoting predicate variables include capital roman letters such as , and , or lower case roman letters, e.g., . In first-order logic, they can be more properly called metalinguistic variables. In higher-order logic, predicate variables correspond to propositional variables which can stand for well-formed formulas of the same logic, and such variables can be quantified by means of second-order quantifiers.
Mbula is an Austronesian language spoken by around 2,500 people on Umboi Island and Sakar Island in the Morobe Province of Papua New Guinea. Its basic word order is subject–verb–object; it has a nominative–accusative case-marking strategy.
The man or boy test was proposed by computer scientist Donald Knuth as a means of evaluating implementations of the ALGOL 60 programming language. The aim of the test was to distinguish compilers that correctly implemented "recursion and non-local references" from those that did not.
There are quite a few ALGOL60 translators in existence which have been designed to handle recursion and non-local references properly, and I thought perhaps a little test-program may be of value. Hence I have written the following simple routine, which may separate the man-compilers from the boy-compilers.
In grammar, a complement is a word, phrase, or clause that is necessary to complete the meaning of a given expression. Complements are often also arguments.
The term predicate is used in two ways in linguistics and its subfields. The first defines a predicate as everything in a standard declarative sentence except the subject, and the other defines it as only the main content verb or associated predicative expression of a clause. Thus, by the first definition, the predicate of the sentence Frank likes cake is likes cake, while by the second definition, it is only the content verb likes, and Frank and cake are the arguments of this predicate. The conflict between these two definitions can lead to confusion.
In linguistics, nominalization or nominalisation is the use of a word that is not a noun as a noun, or as the head of a noun phrase. This change in functional category can occur through morphological transformation, but it does not always. Nominalization can refer, for instance, to the process of producing a noun from another part of speech by adding a derivational affix, but it can also refer to the complex noun that is formed as a result.
Seediq, also known as Sediq, Taroko, is an Atayalic language spoken in the mountains of Northern Taiwan by the Seediq and Taroko people.
The Semantic Web Rule Language (SWRL) is a proposed language for the Semantic Web that can be used to express rules as well as logic, combining OWL DL or OWL Lite with a subset of the Rule Markup Language.
The grammar of Lojban is based on predicate logic. The majority of the grammar is borrowed from the prior "logical language" Loglan, and some of its features come from Láadan. The characteristic regularity, unambiguity, and versatility of Lojban grammar owes much to modern linguistics and computer programming—resources that were unavailable to the designers of earlier languages. Lojbanist Bob LeChevalier summarized one advantage of Lojban grammar as follows: "Lojban moves beyond the restrictions of European grammar. It overtly incorporates linguistic universals, building in what is needed to support the expressivity of the whole variety of natural languages, including non-European ones."
Advanced process monitor (APMonitor) is a modeling language for differential algebraic (DAE) equations. It is a free web-service or local server for solving representations of physical systems in the form of implicit DAE models. APMonitor is suited for large-scale problems and solves linear programming, integer programming, nonlinear programming, nonlinear mixed integer programming, dynamic simulation, moving horizon estimation, and nonlinear model predictive control. APMonitor does not solve the problems directly, but calls nonlinear programming solvers such as APOPT, BPOPT, IPOPT, MINOS, and SNOPT. The APMonitor API provides exact first and second derivatives of continuous functions to the solvers through automatic differentiation and in sparse matrix form.
In linguistics, a catena is a unit of syntax and morphology, closely associated with dependency grammars. It is a more flexible and inclusive unit than the constituent and its proponents therefore consider it to be better suited than the constituent to serve as the fundamental unit of syntactic and morphosyntactic analysis.
The Tseytin transformation, alternatively written Tseitin transformation, takes as input an arbitrary combinatorial logic circuit and produces an equisatisfiable boolean formula in conjunctive normal form (CNF). The length of the formula is linear in the size of the circuit. Input vectors that make the circuit output "true" are in 1-to-1 correspondence with assignments that satisfy the formula. This reduces the problem of circuit satisfiability on any circuit to the satisfiability problem on 3-CNF formulas. It was discovered by the Russian scientist Grigori Tseitin.
The GEKKO Python package solves large-scale mixed-integer and differential algebraic equations with nonlinear programming solvers. Modes of operation include machine learning, data reconciliation, real-time optimization, dynamic simulation, and nonlinear model predictive control. In addition, the package solves Linear programming (LP), Quadratic programming (QP), Quadratically constrained quadratic program (QCQP), Nonlinear programming (NLP), Mixed integer programming (MIP), and Mixed integer linear programming (MILP). GEKKO is available in Python and installed with pip from PyPI of the Python Software Foundation.
A spatial join is an operation in a geographic information system (GIS) or spatial database that combines the attribute tables of two spatial layers based on a desired spatial relation between their geometries. It is similar to the table join operation in relational databases in merging two tables, but each pair of rows is correlated based on some form of matching location rather than a common key value. It is also similar to vector overlay operations common in GIS software such as Intersect and Union in merging two spatial datasets, but the output does not contain a composite geometry, only merged attributes.
Belief merging, also called belief fusion or propositional belief merging, is a process in which an individual agent aggregates possibly conflicting pieces of information, expressed in logical formulae, into a consistent knowledge-base. Applications include combining conflicting sensor information received by the same agent and combining multiple databases to build an expert system. It also has applications in multi-agent systems.
References
- Vasile Rus (2002). Logic Form for WordNet Glosses. Ph.D. thesis, Southern Methodist University.
- Vasile Rus and Dan Moldovan (September 2002). "High performance logic form transformation". International Journal on Artificial Intelligence Tools. 11 (3): 437–454. doi:10.1142/S0218213002000976.
- Dan Moldovan and Vasile Rus (2001). "Logic Form transformation of wordNet and its Applicability to question answering". Proceedings of ACL 2001, Toulouse, France. Archived from the original on 2006-09-13.
- Jerry R. Hobbs (1986). "Overview of the TACITUS project". Computational Linguistics. pp. 12(3).
- Vasile Rus (2004). "A First Evaluation of Logic Form Identification Systems" (PDF). SENSEVAL-3: Third International Workshop on the Evaluation of Systems for the Semantic Analysis of Text. Archived from the original (PDF) on 2005-11-03.
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