J.R. Shoen eld, Mathematical logic, Addison-Wesley Pub., 1967. Home/Search Document Not in Database Summary Related Articles Check |
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Grundlagenstreit in the Theory of Programming - Voda (2003) (Correct)
....that FSI proves jxj n x 2 . 10 5 Theory of De nitions and Modularity We think that the system CL has demonstrated the feasibility of PA as a theory of (concrete) programs. New programs, i.e. computable functions and predicates, are introduced into PA by extensions by de nitions (see [14]) One can show the closure of PA under a rich and comfortable set of clausal de nitions as needed in actual programming. One can then eciently compute the functions and predicates from clausal de nitions [16] When it comes to the questions of modularity, i.e. uniform de nitions where a ....
....de nitions : F (X) Y [X ; Y ] and P (X) X ] where in the former case FSI must prove the existence and uniqueness conditions. Not only are such extensions conservative, but the new symbols are eliminable and so the extended theory cannot prove anything the original theory could not (see [14]) Moreover, the new symbol determines a unique expansion of any model of the original theory. We call such a de nition type one if, in case of functions, FSI proves F (x) 2 V and F (X) 6= 0 X 2 V and, in case of predicates, FSI proves P (X) X 2 V . The reader will note that the type one ....
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J. Shoen eld, Mathematical Logic, Addison-Wesley, 1967.
Partial Safety of Formulas as a Unifying Foundational Principle - Avron (Correct)
....but the intention should be clear. This is a slight generalization of the de nition in [Su98] Suciu s de nition is itself a generalization of the usual de nition ( Ki88,Ul88] which applies only to free Herbrand structures which are generated by adding to some new set of constants. like [Sh67] ) This is what the previous section does. In fact it does more: it provides sucient criteria when a parametric formula de nes a computable nite relation in all domains in which the predicates and functions occurring in it have certain computational properties. We believe that this approach ....
.... insight, we consider rst a conservative extension ZF which is obtained from ZF by adding to it as axioms all sentences of the form 8x 1 ; xn (9 yA(x 1 ; xn ; y) A(x 1 ; xn ; F A;x1 ; x n (x 1 ; xn ) where F A;x1 ; x n is a new function symbol (see [Sh67], section 4.6) De nition 10. Let ZF = f= 2; g, and let ZF f be ZF augmented with all the function symbols of ZF . De ne FZF (2) FZF ( f; f1gg. Extend FZF to ZF f by letting F ZF f (g) f;g for every function symbol g. This de nition means that if x is a variable, and ....
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J. R. Shoen eld, Mathematical Logic, Addison-Wesley, 1967.
An Overview of A Formal Framework For Managing Mathematics - Farmer, Mohrenschildt (2003) (1 citation) (Correct)
....) A 2 ) whenever (A 1 ) and (A 2 ) are de ned. An interpretation of T 1 in T 2 is a translation from T 1 to T 2 such that, for all formulas A of L 1 , if T 1 j= A and (A) is de ned, then T 2 j= A) In other words, an interpretation is a translation that maps theorems to theorems (see [16, 19, 50]) Translations and interpretations are a powerful mechanism for connecting biform theories with similar structure. They serve as conduits for passing information (in the form of formulas) from one theory to another. Translations transport problems (i.e. conjectures) while interpretations ....
Shoen eld, J. R.: 1967, Mathematical Logic. Addison-Wesley.
Deriving Real-time Programs from Duration Calculus.. - Siewe, Van Hung (2000) (6 citations) (Correct)
....and and are true for [t; t ] and [t ] respectively. We consider the following abbreviations: b = 1, ddSee b = P = 0) 3 b = true true, and 2 b = 3: The proof system for DC consists of a complete Hilbert style proof system for rst order logic (cf. e.g. [21]) axioms and rules for interval logic (cf. e.g. 5] Duration Calculus axioms and rules ( 6] and axioms about iteration ( 8] We only recall here some axioms and rules of the proof system of DC . 0 = 0 1 = S 0 S 1 (S 1 S 2 ) S 1 S 2 ) DC5) S = x S ....
J. Shoen eld. Mathematical logic. Addison-Wesley, Reading, Massachusetts, 1967.
On the Expressive Power of Temporal Concurrent.. - Nielsen.. (2002) (1 citation) (Correct)
....Constraint System) Let n 0. De ne FD[n] as the constraint system s.t. is given by the constants symbols 0; 1; n 1 plus the equality = and See [18] for a more general notion of constraints based on Scott s information systems. is given by the axioms for equality ([20]) x = x, x = y ) y = x, x = y y = z ) x = z plus v = w ) false for each two di erent constants v; w in . Intuitively FD[n] provides a theory of variables ranging over a nite domain of values f0; n 1g with syntactic equality over these values. We shall use FD[n] as the underlying ....
J. R. Shoen eld. Mathematical Logic. Addison-Wesley Publishing Company, 1967.
Constraint Logic Programming - Copyright Fran Cois (Correct)
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J.R. Shoen eld, Mathematical logic, Addison-Wesley Pub., 1967.
Paraconsistent Logics and Paraconsistency: Technical and.. - Costa, Krause, Bueno (2004) (Correct)
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Shoen eld, J. R., Mathematical Logic, Reading, Addison-Wesley,
An Equivalence between Second Order Bounded Domain Bounded.. - Razborov (1993) (7 citations) (Correct)
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J. Shoen eld. Mathematical logic. Reading, Mass., AddisonWesley Pub. Co., 1967. Rus. per.: D. Xenfild, Matematiqeska logika, M., Nauka, 1975.
A Formal Framework for Managing Mathematics - Farmer, Mohrenschildt (2001) (1 citation) (Correct)
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J. R. Shoen eld. Mathematical Logic. Addison-Wesley, 1967.
A General Theory of Deduction, Induction, and Learning - Martin, Sharma, Stephan (Correct)
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J. Shoen eld. Mathematical Logic. Addison-Wesley, 1967.
What Can we Gain by Integrating a Language Processor with a.. - Voda (2003) (Correct)
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J. R. Shoen eld. Mathematical Logic, Addison-Wesley, 1967.
Extraction of Efficient Programs in ...-Arithmetic - Komara, Voda (Correct)
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J. R. Shoen eld. Mathematical Logic. Addison-Wesley, 1967.
Predicative Justification and Development of a Second Order Theory .. - Voda (Correct)
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J. Shoen eld, Mathematical Logic, Addison-Wesley, 1967.
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