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One useful logic that defines its own truth
[article]
2008
arXiv
pre-print
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Existential fixed point logic (EFPL) is a natural fit for some applications, and the purpose of this talk is to attract attention to EFPL. ...
The logic is also interesting in its own right as it has attractive properties. ...
As indicated in the introduction, existential fixed-point logic differs from firstorder logic in two respects, the absence of the universal quantifier and the presence of the least-fixed-point operator ...
arXiv:0811.0964v1
fatcat:2npmwx2vubdhpeqz5v7qtzh2ay
Languages which capture complexity classes
1983
Proceedings of the fifteenth annual ACM symposium on Theory of computing - STOC '83
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Vardi, [Va82] , has obtained some nice results on the complexity of languages with added operators including least fixed point and transitive closure. ...
Acknowledgements My ideas for this paper have been clarified during many helpful discussions with friends and colleagues over the past year and a half. ...
The last operator we add in this section is least fixed point, LFP. ...
doi:10.1145/800061.808765
dblp:conf/stoc/Immerman83
fatcat:v4f23jkv25f5jab4oxvifuh4te
RATIONAL DYNAMICS AND EPISTEMIC LOGIC IN GAMES
2007
International Game Theory Review
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Thus, strategic equilibrium gets linked to fixed-points of operations of repeated announcement of suitable epistemic statements. ...
Standard logical analyses of solution sets use assumptions about players in fixed epistemic models for a given game, such as mutual knowledge of rationality. ...
Acknowledgement I thank Krzysztof Apt, Boudewijn de Bruin, Martin Hyland, and two anonymous referees of this Journal for their comments. ...
doi:10.1142/s0219198907001254
fatcat:642kop4v6bcdlmvn4vfbs4qdlm
A Model Checker for Value-Passing Mu-Calculus Using Logic Programming
[chapter]
2001
Lecture Notes in Computer Science
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In particular, we present valuepassing modal mu-calculus, its formal semantics and describe a natural implementation of this semantics as a logic program. ...
Since logic programs naturally deal with variables and substitutions, such an implementation need not pay any additional price-either in terms of performance, or in complexity of implementation-for having ...
We denote least fixed point equations by += and greatest fixed point equations by -=. We also mark the use of formula names by enclosing it in a form(·) constructor. ...
doi:10.1007/3-540-45241-9_1
fatcat:2oelfds5o5agvcch5oeozwmzru
Why not negation by fixpoint?
1988
Proceedings of the seventh ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems - PODS '88
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We also establish that existence of a least fixpoint, for fixed DATALOG' programs, is even harder. ...
In contrast to this, given a DATALOG' program and database values there may be no fixpoint, or a unique lixpoint (and hence a least fixpoint), or even several tixpoints. ...
ACKNOWLEDGMENTS Many thanks to Stavros Cosmadakis, Alex Schatfer, Larry Stockmeyer, Allen Van Gelder, and Moshe Vardi for several useful suggestions and comments on an earlier draft of this paper. ...
doi:10.1145/308386.308446
dblp:conf/pods/KolaitisP88
fatcat:y2dkzkogt5fqxh6pset5zgs7uu
Page 105 of The Monist Vol. 41, Issue 1
[page]
1931
The Monist
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THE PSYCHICAL AND THE LOGICAL IDEA 105
of context, a degree of change and adaptability not to be found in meaning, which is always a fixed, identical ref- erence. ...
And so we may very well ask: Does the “use” of a psychical image mean to refer to its distinction from a significant idea and thus to its existential character, or does its “use” refer to its functioning ...
Why not negation by fixpoint?
1991
Journal of computer and system sciences (Print)
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We also establish that existence of a least fixpoint, for fixed DATALOG' programs, is even harder. ...
In contrast to this, given a DATALOG' program and database values there may be no fixpoint, or a unique lixpoint (and hence a least fixpoint), or even several tixpoints. ...
ACKNOWLEDGMENTS Many thanks to Stavros Cosmadakis, Alex Schatfer, Larry Stockmeyer, Allen Van Gelder, and Moshe Vardi for several useful suggestions and comments on an earlier draft of this paper. ...
doi:10.1016/0022-0000(91)90033-2
fatcat:2uvhfl25ifglpi72et2wijpclq
Constraint Satisfaction, Bounded Treewidth, and Finite-Variable Logics
[chapter]
2002
Lecture Notes in Computer Science
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We systematically investigate the connections between constraint satisfaction problems, structures of bounded treewidth, and definability in logics with a finite number of variables. ...
Finally, we obtain a logical characterization of the property "having bounded treewidth" that sheds light on the complexity-theoretic difference between this property and the property 'being homomorphically ...
Specifically, least fixed-point logic LFP is the extension of first-order logic with least fixed-points of positive first-order formulas. ...
doi:10.1007/3-540-46135-3_21
fatcat:ysssno3exfgvzkg5jl5yaa4kmi
Page 8588 of Mathematical Reviews Vol. , Issue 2001M
[page]
2001
Mathematical Reviews
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For example, they coincide with the equations valid for least-fixed point recursion on cpo’s. ...
This allows us to reason with a number of types of fixed-point equations which heretofore seemed to require metric or order-theoretic ideas. ...
Partial models and logic programming
1986
Theoretical Computer Science
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Each of these semantics takes negation and quantification into account. All three are conservative: they agree with the conventional semantics on pure Horn clause programs. ...
Three extensions of the standard PROLOG fixpoint semantics are presented (called sat, strong, and weak), using partial models, models which may fail to assign truth values to all formulas. ...
We use it in the next section to derive the soundness and completeness of the P-tableau system of Section 10 relative to the least fixed point semantics of [weak] /,. ...
doi:10.1016/0304-3975(86)90096-4
fatcat:2ajyammdifdy5feqp4hjww4vya
The functional dimension of inductive definitions
1992
Theoretical Computer Science
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. it cannot be defined by a second-order formula with existential and universal second-order quantifiers on monadic relations. ...
The functional dimension of an inductive query is the number of independent recursion variables, and is an important logical property of R, related to its efficient evaluation. ...
Let and the arity of the relations is the dimension of the induction. We simply expressed that Q is the least fixed point of the system. ...
doi:10.1016/0304-3975(92)90153-7
fatcat:cftv4hpq35gffninozbbnbqlfq
Euler diagrams as an introduction to set-theoretical models
[article]
2015
arXiv
pre-print
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We show that the model-theoretic notions of validity and invalidity are characterized by Euler diagrams, and, in particular, that model construction can be described as a manipulation of Euler diagrams ...
Understanding the notion of a model is not always easy in logic courses. Hence, tools such as Euler diagrams are frequently applied as informal illustrations of set-theoretical models. ...
This arbitrarily fixes the position of a point from several possibilities. Then, we obtain E from E + S 3 and S 4 . ...
arXiv:1507.03684v1
fatcat:4sdgzgulbngk5m4ne5s7yqidyi
Page 1422 of Mathematical Reviews Vol. , Issue 97C
[page]
1997
Mathematical Reviews
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In particular, an original modelization of the fixed point definition was proposed by K. J. ...
Summary: “Two approaches for defining common knowledge co- exist in the literature: the infinite iteration definition and the circu- lar or fixed point one. ...
Page 5457 of Mathematical Reviews Vol. , Issue 98I
[page]
1998
Mathematical Reviews
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least fixed-point logic and its relatives. ...
In particular, the (K,R)-SFP-game characterizes the stratified fixed-point logic. The results are of interest both for fi- nite model theory and (infinite) model theory. ...
Backward Induction Is PTIME-complete
[chapter]
2013
Lecture Notes in Computer Science
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Obviously, from the least fixed-point definability result it follows that BI is in PTIME [3] . But is it also hard, and therefore complete for PTIME? ...
They have observed that it can be defined in the first-order logic extended with the least fixed-point operator as well as in a variety of other dynamic epistemic formalisms. ...
doi:10.1007/978-3-642-40948-6_32
fatcat:opax6wowxbd3np3z5qynndpa2q
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