Shoenfield, J. R., "Mathematical Logic," Addison-Wesley,1967. Home/Search Document Not in Database Summary Related Articles Check |
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Comparing Expressiveness of Set Constructor Symbols - Dovier, Piazza, Policriti (2000) (Correct)
....Section 4 shows how to apply the results obtained for expressiveness of unification problems and constraints. In Section 5 the results are repeated in the context of multisets. Finally, some conclusions are drawn. 1 Preliminaries We assume standard notions and notation of first order logic (cf. [20]) We use L as a meta variable for first order languages with equality whose variables are denoted by capital letters. We write (X 1 ; Xn ) for a formula of L with X 1 ; Xn as free variables; when the context is clear, we denote a list Z 1 ; Zn of variables by Z. The ....
J. R. Shoenfield. Mathematical Logic. Addison-Wesley, Reading, 1967.
An Equational Re-Engineering of Set Theories - Formisano, Omodeo (1998) (Correct)
.... under different conditions on a certain map P that to every c there corresponds a (superset of a) set of the form P [c] Def fu : vP u for some v2 cg. The former applies when P ( funPart( Q ) designates a function, the latter when r(P ) with P = r(Q )ffi3) designates a total map. [19] adopts a formulation of replacement closer in spirit to the latter, but it is the former that we generalize in what follows. Parameter less replacement, like a parameter less subset axiom scheme, would be of little use. Given an entity d of U , we can think that 0 (d) represents the domain ....
J. R. Shoenfield. Mathematical logic. Addison Wesley, 1967.
Automated Reasoning with Uncertainties - Silva (1992) (Correct)
.... the measures range on real closed fields rather to be read as the probability of selecting a vector of instances for the variables in x that make true a real closed field is a theory with equality containing the functions and Theta and the predicate and obeying the following axioms [Sho67]: 42 than on real numbers. ffl in [AH89, Hal90] the domain of discourse is bounded in size, i.e. it contains a number of elements not greater than a fixed N . Our base language to be extended to contain statistical expressions obeys all these constraints: its domain is always finite and of fixed ....
J. R. Shoenfield. Mathematical Logic. Addison-Wesley, 1967.
On the Expressive Power of Temporal Concurrent Constraint.. - Nielsen, Palamidessi (2002) (1 citation) (Correct)
....#) The following is a very simple finite domain constraint system. Definition 2. A Finite domain Constraint System) Let n 0. Define FD[n] as the constraint system s.t. # is given by the constants symbols 0, 1, n 1 plus the equality = and . # is given by the axioms for equality [19] 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 finite domain of values . n 1 with syntactic equality over these values. We shall use FD[n] as the underlying ....
J. R. Shoenfield. Mathematical Logic. Addison-Wesley Publishing Company, 1967.
Interpretability and Tree Automata: a simple way to solve.. - Seese (1992) (7 citations) (Correct)
....algorithms are drawn. In Section 9 we study local properties. Monadie second order theories are investigated with respect to decidability in Section 10. The article concludes with some remarks and problems. The notation from mathematical logic in this article is standard and can be found e.g. in [Sh67] For a given logic L and a class K of structures for L, the L theory of K, denoted as ThL(N) is the set of all L sentences which are true in K. The monadie second order logic (see further Section 5) results from elementary logic by adding to the corresponding elementary language a sequence of ....
....satisfaction relation G for a given structure G of the corresponding signature with domain A and a given formula whose free individual variables have a given interpretation as elements of A and whose free set variables have a given interpretation as subsets of A. This is done as usual (see e.g. Sh67] by induction on the structure of ffP where the only new case 3X(X) with set variable X is handled as follows: GBXffP(X) iff there isasubset B of A such that G [B] where B is chosen as interpretation of X Universal quantification and the usual set operators and relations can now be defined ....
J.R. Shoenfield 1967, Mathematical Logic, Reading, Addison Wesley.
Dynamic Logic - Harel, Kozen, Tiuryn (1984) (356 citations) (Correct)
.... Logic, was developed by [Constable, 1977] Dynamic Logic, which emphasizes the modal nature of the program assertion interaction, was introduced by [Pratt, 1976] Background material on mathematical logic, computability, formal languages and automata, and program verification can be found in [Shoenfield, 1967] (logic) Rogers, 1967] recursion theory) Kozen, 1997a] formal languages, automata, and computability) Keisler, 1971] infinitary logic) Manna, 1974] program verification) and [Harel, 1992; Lewis and Papadimitriou, 1981; Davis et al. 1994] computability and complexity) Much of this ....
J. R. Shoenfield. Mathematical Logic. Addison-Wesley, 1967.
A Gentle Introduction to the Universal Algorithmic Agent AIXI - Hutter (2003) (2 citations) (Correct)
....and axioms, and inference rules. A proof is a sequence of formulas, where each formula is either an axiom or inferred from previous formulas in the sequence by applying the inference rules. Details can be found in [Hut02a] in a related construction or in any textbook on logic or proof theory, e.g. [Fit96, Sho67]. We only need to know that provability and Turing Machines can be formalized. The setup time in the main theorem is just the time needed to verify the 2 proofs, each needing time O(l P ) 6.7 Limitations and Open Questions . Formally, the total computation time of p # for cycles 1. k ....
J. R. Shoenfield. Mathematical logic. Addison-Wesley, 1967.
Active Logics: A Unified Formal Approach to Episodic.. - Elgot-Drapkin, Kraus, .. (Correct)
....of finding an actual chain of inferences constituting a proof of a formula of interest, one might instead be able to show that all models satisfy the formula, which establishes the existence of a proof. This however not only can be a useful way to circumvent proof construction, it also serves [ Shoenfield, 1967 ] to give insights into the structure of the theorem set. In the case of Agenta, a completeness theorem allows us another way to think about and assess his beliefs. Such is very useful, for instance in NMR, where comparison between T 1 and T 2 is often made semantically, i.e. their theorem sets ....
J. R. Shoenfield. Mathematical Logic. Addison Wesley, Reading, MA, 1967.
The Formal and Computational Theory of Complex Constraint.. - Damas, Moreira, Varile (1994) (Correct)
....and variables respectively, we define the terms T of our theory in the usual way as being the least set such that: 1. elements of V are in T 2. for f in F and t 1 , t n in T , f t 1 , t n is in T Function symbols come equipped with their arity n written as f . See [Sho67] for an introduction to first order theories. We will see below how we will restrict the interpretation of the elements of T to decidable algebrae. 1.2 Constraint Language We define the constraint language L over T as being the usual first order language with the equality as the only ....
Shoenfield, Joseph R., 1967. Mathematical Logic. AddisonWesley.
Heterogeneous Active Agents, I: Semantics - Eiter, Subrahmanian, Pick (1999) (4 citations) (Correct)
....the value. Definition 2.2 (code call atom) If cc is a code call, and X is either a variable symbol, or an object of the output type of cc, then in(X; cc) is a code call atom. 2 Code call atoms, when evaluated, return boolean values (i.e. they may be thought of as special types of logical atoms [90]) Intuitively, a code call atom succeeds just in case X is in the result set 6 returned by cc (when X is an object) or when X can be made to point to one of the objects returned by executing the code call. Let us return to the code calls we introduced earlier, and see examples of some code call ....
J. Shoenfield. Mathematical Logic. Addison Wesley, 1967.
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Shoenfield, J. R., "Mathematical Logic," Addison-Wesley,1967.
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J. R. Shoenfield. Mathematical Logic. Addison--Wesley, 1967.
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J. Shoenfield. Mathematical Logic. Addison-Wesley, Reading, Massachusetts, 1967.
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Shoenfield, J. R. Mathematical Logic. Addison-Wesley, Reading, Mass., 1967, Sec. 1.2, pp. 2--6.
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J.R. Shoenfield. Mathematical logic. Addison Wesley (1967).
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J.R. Shoenfield, Mathematical Logic (Addison-Wesley, Reading, MA, 1967).
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Shoenfield, J. Mathematical Logic. Addison-Wesley, 1967.
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:].R. Shoenfield, Mathematical Logic, (Addison-Wesley, Reading, Mass, 1967) 74- 75.
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