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Forcing (Model theory) --- Axiomatic set theory --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory --- Axioms --- Logic, Symbolic and mathematical --- Set theory --- Model theory

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Forcing (Model theory) --- Axiomatic set theory --- Mathematics --- Physical Sciences & Mathematics --- Mathematical Theory

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Computer science --- Logic, Symbolic and mathematical. --- Logique symbolique et mathématique --- Logic, symbolic and mathematical --- 511.3 --- 681.3*F41 --- Analytical, additive and other number-theory problems. Diophantine approximations --- Mathematical logic: computability theory; computational logic; lambda calculus; logic programming; mechanical theorem proving; model theory; proof theory;recursive function theory--See also {681.3*F11}; {681.3*I22}; {681.3*I23} --- 681.3*F41 Mathematical logic: computability theory; computational logic; lambda calculus; logic programming; mechanical theorem proving; model theory; proof theory;recursive function theory--See also {681.3*F11}; {681.3*I22}; {681.3*I23} --- 511.3 Analytical, additive and other number-theory problems. Diophantine approximations --- Logic, Symbolic and mathematical --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism

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Time is ubiquitous in information systems. Almost every enterprise faces the problem of its data becoming out of date. However, such data is often valu­ able, so it should be archived and some means to access it should be provided. Also, some data may be inherently historical, e.g., medical, cadastral, or ju­ dicial records. Temporal databases provide a uniform and systematic way of dealing with historical data. Many languages have been proposed for tem­ poral databases, among others temporal logic. Temporal logic combines ab­ stract, formal semantics with the amenability to efficient implementation. This chapter shows how temporal logic can be used in temporal database applica­ tions. Rather than presenting new results, we report on recent developments and survey the field in a systematic way using a unified formal framework [GHR94; Ch094]. The handbook [GHR94] is a comprehensive reference on mathematical foundations of temporal logic. In this chapter we study how temporal logic is used as a query and integrity constraint language. Consequently, model-theoretic notions, particularly for­ mula satisfaction, are of primary interest. Axiomatic systems and proof meth­ ods for temporal logic [GHR94] have found so far relatively few applications in the context of information systems. Moreover, one needs to bear in mind that for the standard linearly-ordered time domains temporal logic is not re­ cursively axiomatizable [GHR94]' so recursive axiomatizations are by necessity incomplete.

Computer logic. --- Database management. --- Logique informatique --- Bases de données --- Gestion --- Computer logic --- Database management --- 681.3*F41 --- 681.3*H0 --- Data base management --- Data services (Database management) --- Database management services --- DBMS (Computer science) --- Generalized data management systems --- Services, Database management --- Systems, Database management --- Systems, Generalized database management --- Electronic data processing --- Computer science logic --- Logic, Symbolic and mathematical --- Mathematical logic: computability theory; computational logic; lambda calculus; logic programming; mechanical theorem proving; model theory; proof theory;recursive function theory--See also {681.3*F11}; {681.3*I22}; {681.3*I23} --- Computerwetenschap--?*H0 --- 681.3*F41 Mathematical logic: computability theory; computational logic; lambda calculus; logic programming; mechanical theorem proving; model theory; proof theory;recursive function theory--See also {681.3*F11}; {681.3*I22}; {681.3*I23} --- Bases de données --- Data structures (Computer science). --- Artificial intelligence. --- Programming languages (Electronic computers). --- Information storage and retrieval. --- Data Structures and Information Theory. --- Artificial Intelligence. --- Programming Languages, Compilers, Interpreters. --- Information Storage and Retrieval. --- Computer languages --- Computer program languages --- Computer programming languages --- Machine language --- Languages, Artificial --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Information structures (Computer science) --- Structures, Data (Computer science) --- Structures, Information (Computer science) --- File organization (Computer science) --- Abstract data types (Computer science)