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Semantical characterizations and complexity of equivalences in answer set programming

2007
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ACM Transactions on Computational Logic
*

*complexity*. ... For all these notions, we consider disjunctive

*logic*programs in the propositional (ground) case as well as some restricted

*classes*, providing semantical characterizations and analyzing the computational ... would like to thank David Pearce for interesting discussions and comments about this work and pointers to related literature, as well as Katsumi Inoue and Chiaki Sakama for their valuable remarks on

*relativizing*...

##
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Semantical Characterizations and Complexity of Equivalences in Answer Set Programming
[article]

2005
*
arXiv
*
pre-print

*complexity*. ... For all these notions, we consider disjunctive

*logic*programs in the propositional (ground) case, as well as some restricted

*classes*, provide semantical characterizations and analyze the computational ... would like to thank David Pearce for interesting discussions and comments about this work and pointers to related literature, as well as Katsumi Inoue and Chiaki Sakama for their valuable comments on

*relativizing*...

##
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Martin's Conjecture: A Classification of the Naturally Occurring Turing Degrees

2019
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Notices of the American Mathematical Society
*

Computability Theory Computability theory is the area of

doi:10.1090/noti1940
fatcat:gfm5r4rsezc5tda3y2myytt5su
*logic*that studies the*complexity*of infinite countable objects. ... 1 1 0 1 0 1 0 0 1 0 1 1 S Antonio Montalbán This paper is about naturally occurring objects in computability theory, the area inside mathematical*logic*that studies the*complexity*of infinite countable ...##
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Page 5097 of Mathematical Reviews Vol. , Issue 2000g
[page]

2000
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Mathematical Reviews
*

which characterizes ACp as the non-

*uniformly*first-order definable*classes*of finite structures. ... The significance of our investigation is conceptual, rather than technical: We identify ex- actly the*logical*analogue of uniform and non-uniform*complexity**classes*.” ...##
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Page 7301 of Mathematical Reviews Vol. , Issue 97M
[page]

1997
*
Mathematical Reviews
*

Pnueli,

*Logics**capturing**relativized**complexity**classes**uniformly*(463-479); Eric Rosen and Scott Weinstein, Preservation theorems in finite model theory (480-502); Dan Suciu and Val Breazu-Tannen, A query ... {The papers will not be reviewed individually. } 97m:03005 03-06 03D15 68-06 68Q05 68Q15 % Workshop on Computability,*Complexity*and*Logic*. ...##
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Relativized depth
[article]

2021
*
arXiv
*
pre-print

oracles the

arXiv:2112.04451v1
fatcat:e2mxyubyrrhz5pmwdflllewn34
*relativized**class*is contained in the unrelativized*class*. ... Accordingly, for most notions for sets considered in computability theory, for the corresponding*classes*trivially for all oracles the unrelativized*class*is contained in the*relativized**class*or for all ... This situation is*captured*quite well within the framework of depth. ...##
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Fixed-point logics, generalized quantifiers, and oracles

1997
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Journal of Logic and Computation
*

On ordered structures, where our results still hold, this reads as follows: For any given oracle Q, the

doi:10.1093/logcom/7.3.405
fatcat:ti26eh7bzrczda33ejnlm3n3ju
*complexity**class*PTIME Q (or PSPACE Q in a bounded oracle model) can be characterized by an extension ... However, there is no such*logic*L that satis es L(Q) PTIME Q (or PSPACE Q ) for all Q. We also study second order*logic*. Each level i of the polynomial hierarchy has a complete circuit problem. ... So, one could ask brie y: Is there a Lindstr om*logic*for oracle*complexity**classes*? ...##
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Model-Theoretic Characterizations of Boolean and Arithmetic Circuit Classes of Small Depth
[article]

2017
*
arXiv
*
pre-print

In this paper we give a characterization of both Boolean and arithmetic circuit

arXiv:1710.01934v2
fatcat:2haqhvlugzhv5mrzh3jp334y64
*classes*of logarithmic depth in the vein of descriptive*complexity*theory, i.e., the Boolean*classes*NC^1, SAC^1 and AC^1 ... We build on Immerman's characterization of constant-depth polynomial-size circuits by formulas of first-order*logic*, i.e., AC^0 = FO, and augment the*logical*language with an operator for defining relations ... To further show the robustness of our*classes*, we want to mention certain variations of our*logics*that do not change the resulting*complexity**classes*. ...##
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A Common View on Strong, Uniform, and Other Notions of Equivalence in Answer-Set Programming
[article]

2007
*
arXiv
*
pre-print

Moreover,we provide

arXiv:0712.0948v1
fatcat:kgshzsszgbe3fklcwwpdkyczki
*complexity*bounds for the problem in question and sketch a possible implementation method. To appear in Theory and Practice of*Logic*Programming (TPLP). ...*Logic*programming under the answer-set semantics nowadays deals with numerous different notions of program equivalence. ... The*class*of all*logic*programs (over the fixed universe U) is denoted by C U . ...##
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Parameter free induction and provably total computable functions

1999
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Theoretical Computer Science
*

with the

doi:10.1016/s0304-3975(98)00305-3
fatcat:an5vkane5beidkzgxwvziybb4q
*class*of doubly recursive functions of Peter. ... These results are based on a precise characterization of ZC; and Zw in terms of reflection principles and conservation results for local reflection principles obtained by techniques of modal provability*logic*... The above example of a natural pair of theories*capturing*the same*class*of computable functions, whose union*captures*a much bigger*class*, opens the question whether there may exist in general a unique ...##
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Decidable Theories of the Ordering of Natural Numbers with Unary Predicates
[chapter]

2006
*
Lecture Notes in Computer Science
*

Expansions of the natural number ordering by unary predicates are studied, using

doi:10.1007/11874683_37
fatcat:3b443nbf65d7fer6qzxvxqhbvy
*logics*which in expressive power are located between first-order and monadic second-order*logic*. ... a*class*of*logics*between first-order*logic*and monadic*logic*. ... There is a recursive*uniformly*homogeneous set for M with respect to the monadic (second-order)*logic*. ...##
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How to define a linear order on finite models

1997
*
Annals of Pure and Applied Logic
*

We carry out a systematic investigation of the definability of linear order on

doi:10.1016/s0168-0072(97)00008-0
fatcat:5h4r4lawurdh5fknxdhrmxbafm
*classes*of finite rigid structures. ... PFP, infinitary*logic*Z! ...*capturing*the*complexity**class*. ...##
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A common view on strong, uniform, and other notions of equivalence in answer-set programming

2008
*
Theory and Practice of Logic Programming
*

Moreover, we provide

doi:10.1017/s1471068407003250
fatcat:gaifw5b4cfgdncrrp7glsdexei
*complexity*bounds for the problem in question and sketch a possible implementation method making use of dedicated systems for checking ordinary equivalence. ... theoretical tools to compare incomplete programs and are defined by either restricting the syntactic structure of the considered context programsRor by bounding the set$\A$of atoms allowed to occur inR(*relativized*... The*class*of all*logic*programs over universe U is denoted by C U . ...##
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Equivalence between answer-set programs under (partially) fixed input

2017
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Annals of Mathematics and Artificial Intelligence
*

We give full characterization results and a

doi:10.1007/s10472-017-9567-5
fatcat:qq2txtfykvg7li75euqt3wfppq
*complexity*analysis for the propositional case of rule equivalence and its*relativized*versions. ... Among the huge body of theoretical results, investigations of different equivalence notions between*logic*programs play a fundamental role for understanding modularity and optimization. ... to the*class*of unary programs. ...##
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Discriminative Gaifman Models
[article]

2016
*
arXiv
*
pre-print

Considering local and bounded-size neighborhoods of knowledge bases renders

arXiv:1610.09369v1
fatcat:tvvlmhv27vf2zkzhjiwbqnqb3u
*logical*inference and learning tractable, mitigates the problem of overfitting, and facilitates weight sharing. ... We can now state the following*complexity*result. d = (d 1 , ..., d n ), generated neighborhood N ∈ N r,k (d), and ϕ i ∈ Φ, we perform the substitution [s 1 /d 1 , ..., s n /d n ] and*relativize*ϕ i 's ... The expected probability of a representation of a neighborhood drawn*uniformly*at random from N (r,k) (d). ...
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