J. Barwise and S. Feferman, editors. Model-Theoretic Logics. Springer, 1985.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....3. Other second order quantifiers: Measure theoretic quantifiers, and topological logics. Barwise, Makkai, Kaufmann, Flum, Ebbinghaus and Ziegler. 4. Other logics: Monadic logics. Rabin, Gurevich, B uchi, Shelah. There are many more logics, see the volume edited by Jon Barwise and Solomon Feferman [BaFe]. There is a particularly rich model theory for L(Q) In the last 20 years, this theory took on a set theoretic flavor, see: Fuhrken [Fur] Keisler [Ke1] Sh 82] Gr2] and [HLSh] For an overview of some of this I recommend Wilfrid Hodges s book [Ho1] A common feature of all the above ....

....concepts like continuity, differentiability, analyticity, and their relations would remain at best vaguely perceived. It is only the study of more general functions that one sees the importance of these notions, and their different roles, even for the simple case. Jon Barwise, page 15 16 of [BaFe]. 2. It is beautiful and difficult mathematics. 3. Effect on model theory for first order theories. Already [Sh87a] and [Sh87b] had a profound effect on the proof of main gap for first order theories. Especially good sets and stable systems. See the last 5 sections of Chapter XII in [Sh c] and ....

K. Jon Barwise and Solomon Fefferman (Ed.). Model theoretic logics, Springer-Verlag 1985.

....3. Some proof systems, especially those containing an existential instantiation rule, make the dependencies explicit by using instantial terms indexed by the parameters (typically obtained by universal instantiation) on which the term depends. A nice overview of such systems is contained in Fine [1985] (cf. also de Queiroz and Gabbay [1995] It is claimed here that introducing dependence explicitly into first order logic, as indices on variables, allows one to formulate distinctions not otherwise expressible; in particular, generalized quantifiers will be seen to arise from various forms of ....

....(5) vy yVx vy. It is well known that the proof theory of this quantifier presents considerable dculties. Since interpolation fails for co countably many, it was conjectured that there is no good sequent calculus for the full axioms (see e.g. BarMse s introduction to Barwise and Feferman [1985]) We show here that there does exist a sequent calculus for co countably many, formulated in the language of indexed variables. The rule which corresponds to (5) is a substitution rule which licenses substitution of an indexed variable under certain restrictions. However, to derive (5) from ....

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K. J. Barwise and S. Feferman (editors), Model-theoretic logics, Springer-Verlag.

....Modular logic programming proves to be a rich formalism whose expressiveness and complexity can be controlled by efficiently recognizable syntactic restrictions. 1 Introduction Generalized quantifiers are a well known concept for enhancing the expressive capabilities of a logical language [44, 34, 7, 59]. They have been introduced since in many contexts, the standard quantifiers for all individuals and for some individual are not strong enough for a proper description of the state of affairs. Informally, a generalized quantifier Qx is a collection C of structures for a language L, and Qx (x; ....

J. Barwise and S. Feferman. Model-Theoretic Logics. Springer, 1985.

....or three variable fragment of first order logic (over the same vocabulary) Two remarks are in order. First, As an aside, the difference between our definition and Baader s is analogous to the difference between definability and projective definability in the area of model theoretic logics; see [Barwise and Feferman, 1985] . it is well known that there is a correspondence between some description logics and modal logics (see [ Schild, 1991 ] and modal logicians have considered the links with finite variable fragments for quite some time (see [ Gabbay, 1981 ] Thus, Borgida s results could also have been ....

J. Barwise and S. Feferman, editors. Model-Theoretic Logics. SpringerVerlag, 1985.

....many intimate connections between logic and topology have been established and studied, it seems that topological methods and results have so far been under utilized for solving purely logical problems. Besides extensive research on abstract model theory involving topological machinery (see [Barwise and Feferman, 1985]) I am aware of not many other publications, such as [Rasiowa and Sikorski, 1963]and[Goldblatt, 1985] which more explicitly pursue that direction. In this paper we begin systematic exploration of the idea of using basic topological techniques and results to obtain relative completeness results in ....

Barwise J. and S. Feferman (eds.) ModelTheoretic Logics, Springer-Verlag, 1985.

....the syntax of rst order logic with in nitary formation rules or with xpoint operators that act as iteration constructs. In this section we consider certain in nitary logics and investigate their relation to Datalog(6= During the 1960s and the 1970s logicians investigated in depth (cf. [BF85]) the in nitary logic L1 , which, in addition to the rules of rst order logic, allows for disjunctions W and conjunctions V over any (possibly in nite) set of formulas. More formally, the syntax of the in nitary logic L1 is de ned as follows. De nition 3.1: Let be a vocabulary ....

J. Barwise and S. Feferman, editors. Model-Theoretic Logics. Springer-Verlag, 1985.

....formula stating that there exist precisely k unions u of equality types that satisfy . More formally, F (n) k ( J U jJj=k u2J (ff u =T ) u2(U GammaJ ) ff u =T ) Thus, the set fn : F (n) kg is definable in L. Remark. We use the term logic here in the sense of model theory (see [4]) Our definition is very liberal: a logic L associates with each vocabulary a set L( of sentences and a satisfaction relation j= between structures and sentences 2 L( Depending on the context, some conditions may be imposed, e.g. that L( be recursive. One condition always present, and ....

....in first order logic is also explicitly first order definable, i.e. definable by a formula (x) such that Q(A) fa : A j= a)g for every A 2 C. There also has been considerable effort in model theory to investigate the status of analogues to Beth s Theorem for more powerful logics than FO (see [4]) For first order logic, Beth s result mostly serves as an excuse to disregard implicit definitions, since they don t give additional expressiveness. However, on finite structures, Beth s Theorem fails, and implicit definitions provide more expressive power than explicit ones. In fact, implicit ....

J. Barwise and S. Feferman, eds., Model-Theoretic Logics, Springer-Verlag, 1985.

....formulas. 1 1 Introduction Recently, there has been considerable interaction between database theory and finite model theory [F90] A particularly useful formalism developed in finite model theory is infinitary logic, an extension of first order logic with infinite conjunctions and disjunctions [BF85]. Infinitary logic with finitely many variables (denoted L 1 ) see [Ba77] provides an elegant framework for studying important phenomena such as 0 1 laws [KV90b] and expressive power of query languages [ACY91, KV90a] While infinitary logic is an elegant theoretical tool, infinitary logic ....

Barwise, J., S. Feferman (eds.), Model-Theoretic Logics, Springer-Verlag, 1985.

.... theory The approach of this paper is abstract model theory in roughly the same spirit as the Hungarian School (e.g. 1] which means much more than the familiar logical tradition of abstracting Tarskian semantics to extend classical first order model theory towards other logical systems [3, 2]. The CB framework is closer to the theory of institutions [19] in that: ffl it parameterises over signatures, rather than assuming a fixed signature given in advance; ffl it abstracts Tarski s semantic definition of truth [48] to a (functorial) relation of satisfaction between models and ....

Jon Barwise and Solomon Feferman. Model-Theoretic Logics. Springer, 1985.

....as the work by the Hungarian School in late seventies, 10 for example, is characterized as abstract model theory. By abstract model theory (abbreviated AMT) we mean far more than the respective tradition in logic which abstracts the Tarskian approach to cover other logical systems 11 (e.g. [6, 5]) Our category based framework is very close in spirit to the theory of institutions [33] in the sense that ffl it abstracts Tarski s classic semantic definition of truth [93] based on a relation of satisfaction between models and sentences, and ffl it uses category theory in a very similar ....

Jon Barwise and Solomon Feferman. Model-Theoretic Logics. Springer, 1985.

....for each sentence # # L[L] there exists a sentence # r # L[L] such that M L = # if and only if M r L = # r . The field of abstract model theory originated with P. Lindsrom s landmark paper [12] and thrived during the 1970 s. For an introduction to the subject we refer the reader to [2]. 4 JOS E IOVINO A logic L has conjunctions if for every pair of sentences #, # # # L[L] there exists a sentence # # L[L] such that M L = # if and only if M L = # and M L = # # . The logic L is said to have negations if for every sentence # # L[L] there exists a sentence # # ....

J. Barwise and S. Feferman, editors. Model-theoretic logics. Springer-Verlag, New York, 1985.

....and soundness of the equational deduction system with respect to its model theory. 1. 2 Abstract model theory By abstract model theory (abbreviated as AMT) we mean far more than the respective tradition in logic which abstracts the Tarskian approach to cover other logical systems 2 (e.g. [4, 3]) Our AMT framework is very close in spirit to the theory of institutions [17] in the sense that ffl it abstracts Tarski s classic semantic definition of truth [39] based on a relation of satisfaction between models and sentences, and ffl it uses category theory in a very similar manner to ....

Jon Barwise and Solomon Feferman. Model-Theoretic Logics. Springer, 1985.

....in Figure 2, our mathematical findings corroborate the intuitions one has concerning the expressive power of description logics; we view this as additional evidence in support of our methods. difference between definability and projective definability in the area of model theoretic logics; see [BF85]. 23 It should be noted that the role of our semantic characterization results is in separating the expressive power of description logics, not in showing that they coincide with respect to their expressive power. For the latter, we use explicit syntactic definitions of the constructions of one ....

J. Barwise and S. Feferman, editors. Model-Theoretic Logics. Springer-Verlag, 1985.

....forms of games cannot handle these without more radical alterations. 2.3. Games in mathematics. In mathematics, game conceptualisations are not usually purely semantic, but may belong to the category of comparison and cutand choose games. They are often resorted to in abstract model theory (cf. [Barwise, 1985]) Many ideas go back to analytic games (Borel games) introduced by Gale and Stewart [Gale Stewart, 1953] as well as to Banach Mazur games. In Ehrenfeucht Fra ss e ( rst order) comparison games, one can prove equivalences in nite structures. There are two players, the spoiler and the ....

Barwise, J. and Feferman, S., (eds.), (1985) Model Theoretic Logics, Perspectives in Mathematical Logic, Berlin: Springer.

....most of those tools developed are modified Ehrenfeucht Fraisse games, whose application often involves a rather intricate argument. Furthermore, most current tools are applicable only to firstorder logic and some of its extensions (like fragments of second order logic [15] infinitary logics [5], logics with counting [20] etc. but they do not apply to languages that resemble real query languages, like SQL. The goal of this paper is to give a thorough study of local properties of queries in a context that goes beyond the pure first order case, and then apply the resulting tools to ....

J. Barwise et al eds., Model-Theoretic Logics. Springer-Verlag, 1985.

....R 1 ; R u ) for such a structure A. A generalized quantifier or a model class of (similarity) type t is any class Q of structures of type t so that Q is closed under isomorphisms. Every (generalized) quantifier Q gives rise to a natural logical operation Q. We refer to [Lin66] and [BF85] for the definition of this operation. This leads to the concept of definablity of quantifiers: A quantifier Q is definable in terms of quantifiers Q 1 ; Q n if Q is the class of all models of a sentence of the extension of first order logic by the logical operations Q 1 ; ....

J. Barwise and S. Feferman (eds.). Model-Theoretic Logics. Springer, 1985.

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J. Barwise and S. Feferman, editors. Model-Theoretic Logics. Springer, 1985.

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J. Barwise et al eds., Model-Theoretic Logics. Springer-Verlag, 1985.

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J. Barwise, S. Feferman, editors. Model-Theoretic Logics. Springer-Verlag, 1985.

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Barwise, J. and S. Feferman (Eds.), ModelTheoretic Logics. Springer-Verlag, Berlin. 1985.

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J. Barwise and S. Feferman, editors. Model-Theoretic Logics. Springer-Verlag, 1985.

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J. Barwise and S. Feferman. Model-Theoretic Logics. Springer, New York, 1985.

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J. Barwise and S. Feferman, editors. Model-Theoretic Logics. Springer{Verlag, Berlin, 1985.

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Barwise, J., S. Feferman (eds.), Model-Theoretic Logics, Springer-Verlag, 1985.

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J. Barwise, S. Feferman (Eds.), Model-Theoretic Logics, Springer Verlag, Berlin, (1985).

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