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Strong equivalence of logic programs under the infinite-valued semantics

2009
*
Information Processing Letters
*

We consider

doi:10.1016/j.ipl.2009.02.002
fatcat:dflenb4w2jgotf5px6npcxcyey
*the*notion*of**strong**equivalence*[4]*of*normal propositional*logic**programs**under**the**infinite*-*valued**semantics*[7] (which is a purely model-theoretic*semantics*that is compatible with*the*... We demonstrate that two such*programs*are strongly*equivalent**under**the**infinite*-*valued**semantics*if and only if they are*logically**equivalent*in*the**infinite*-*valued**logic**of*[7] . ...*Strong**Equivalence**under**the**Infinite*-*Valued**Semantics*In this section we demonstrate that*strong**equivalence**under**the**infinite*-*valued**semantics*corresponds to*logical**equivalence*in*infinite*-*valued**logic*...##
###
A Sufficient Condition for Strong Equivalence Under the Well-Founded Semantics
[chapter]

2005
*
Lecture Notes in Computer Science
*

We consider

doi:10.1007/11562931_35
fatcat:3evcqjuzdfe7vbppeqlhw52f3q
*the*problem*of**strong**equivalence*[1]*under**the**infinite*-*valued**semantics*[2] (which is a purely model-theoretic version*of**the*well-founded*semantics*). ... We demonstrate that two*programs*are now strongly*equivalent*if and only if they are*logically**equivalent**under**the**infinite*-*valued**logic**of*[2] . ... Main Technical Results Our first result states that*the*notion*of**strong**equivalence**under**the**infinite*-*valued**semantics*coincides with*the*notion*of**logical**equivalence**under**the**infinite*-*valued**logic*...##
###
Strong Equivalence of Logic Programs with Ordered Disjunction: a Logical Perspective
[article]

2022
*
arXiv
*
pre-print

In this paper we obtain a purely

arXiv:2205.04882v1
fatcat:u2egr7c4ybhybgnpblxzdyopai
*logical*characterization*of**strong**equivalence**of*LPODs as*logical**equivalence*in a four-*valued**logic*. ... This comes in sharp contrast with*the*well-known characterization*of**strong**equivalence*for classical*logic**programs*, which, as proved by Lifschitz et al. (2001), coincides with*logical**equivalence*in ... Two*logic**programs*P 1 and P 2 are termed strongly*equivalent**under*a given*semantics*if for every*logic**program*P , P 1 ∪ P has*the*same meaning as P 2 ∪ P*under*this given*semantics*. ...##
###
Strong Equivalence of Logic Programs with Ordered Disjunction: A Logical Perspective

2022
*
Theory and Practice of Logic Programming
*

In this paper we obtain a purely

doi:10.1017/s1471068422000242
fatcat:ryqzjtfac5bndfgilefnz2pqni
*logical*characterization*of**strong**equivalence*for LPODs as*logical**equivalence*in a four-*valued**logic*. ... This comes in sharp contrast with*the*well-known characterization*of**strong**equivalence*for classical*logic**programs*, which coincides with*logical**equivalence*in*the**logic**of*here-and-there. ... Two*logic**programs*P 1 and P 2 are termed strongly*equivalent**under*a given*semantics*if for every*logic**program*P , P 1 ∪ P has*the*same meaning as P 2 ∪ P*under*this given*semantics*. ...##
###
Contents and abstracts of the electronic notes in Theoretical Computer Science Vol. 5

1998
*
Theoretical Computer Science
*

Monica Nesi
Mechanising a modal

doi:10.1016/s0304-3975(97)00248-x
fatcat:sdn5br4hkvhjnowkexgso4rute
*logic*for*value*>passing agents in HOL http://wwu.elsevier.nl/locate/entcs/volume5.html An extension*of*Hennessy-Milner*logic*to*value*-passing CCS is embedded in*the*HOL ... They are used to compute static properties verified by*the*standard concurrent execution*of**the**program*by means*of*abstract model-checking*of*modal*logic*formulae. ... For this*logic*we present a proof system for model checking sequential processes defined in*the**value*-passing CCS. ...##
###
Page 6048 of Mathematical Reviews Vol. , Issue 2002H
[page]

2002
*
Mathematical Reviews
*

Our aim is to provide a

*semantic*foundation for*the*development*of*a general, suitable, and accurate framework for*the*analysis*of*functional*logic**programs*.” 2002h:68029 68N18 Hinze, Ralf (D-BONN-I3; ... Summary: “We introduce a*semantic*characterization*of*narrow- ing,*the*computational engine*of*many functional*logic*languages. ...##
###
Department of Computer Science

1993
*
Journal of Computational and Applied Mathematics
*

In addition we axiomatise

doi:10.1016/0377-0427(93)90083-n
fatcat:e3qojetr5re5rpb2alwd6g7ky4
*the**logic**of*HT 2 -models and prove that it captures*the**strong**equivalence**of*theories in partial equilibrium*logic*. ... We propose a solution to a long-standing problem in*the*foundations*of*well-founded*semantics*(WFS) for*logic**programs*. ... Note that unlike in*the*case*of**strong**equivalence**under*stable model*semantics*, we cannot assume in*the*general case that*the*formulas in Γ have*the*syntax*of**logic**program*rules. ...##
###
Department of Computer Science

1991
*
Journal of Computational and Applied Mathematics
*

In addition we axiomatise

doi:10.1016/s0377-0427(91)90073-s
fatcat:is7milsu65bhjnqmhk7ei5nfbq
*the**logic**of*HT 2 -models and prove that it captures*the**strong**equivalence**of*theories in partial equilibrium*logic*. ... We propose a solution to a long-standing problem in*the*foundations*of*well-founded*semantics*(WFS) for*logic**programs*. ... Note that unlike in*the*case*of**strong**equivalence**under*stable model*semantics*, we cannot assume in*the*general case that*the*formulas in Γ have*the*syntax*of**logic**program*rules. ...##
###
On the Relation between Weak Completion Semantics and Answer Set Semantics
[article]

2019
*
arXiv
*
pre-print

*The*underlying three-

*valued*

*logic*

*of*both

*semantics*is different and their models are evaluated with respect to different

*program*transformations. ... In particular, we will show that

*logic*

*programs*

*under*

*the*WCS can be represented as

*logic*

*programs*

*under*

*the*ASP by means

*of*a definition completion, where all defined atoms in a

*program*must be false ... We are thankful to David Pearce for pointing to Vakarelov's work on

*the*relation between Lukasiewicz

*logic*and classical

*logic*with

*strong*negation. ...

##
###
On the relations between stable and well-founded semantics of logic programs

1992
*
Theoretical Computer Science
*

Two-

doi:10.1016/0304-3975(92)90285-n
fatcat:nlng3ns3are37ilruxydzvlouu
*valued**strong*completion specifies*the*stable*semantics*. l Three-*valued**strong*completion specifies*the*well-founded*semantics*. (3) We study*the**equivalence*between stable*semantics*and well-founded ... ., On*the*relations between stable and well-founded*semantics**of**logic**programs*, Theoretical Computer Science 105 (1992) 7-25. ... I am also grateful to*the*anonymous referees for their comments pointing out many shortcomings*of**the*previous versions*of*this paper. ...##
###
Logic Programs under Three-Valued Łukasiewicz Semantics
[chapter]

2009
*
Lecture Notes in Computer Science
*

If

doi:10.1007/978-3-642-02846-5_37
fatcat:4cyqxgzccvg5rbuopd3appqbom
*logic**programs*are interpreted over a three-*valued**logic*, then often Kleene's*strong*three-*valued**logic*with complete*equivalence*and Fitting's associated immediate consequence operator is used. ... In this paper, we consider*the*three-*valued*Lukasiewicz*semantics*and show that fixed points*of**the*Fitting operator are also models for*the**program**under*consideration and that*the*model intersection ... Acknowledgement*The*authors would like to thank Bertram Fronhöfer for many fruitful discussions. ...##
###
Optimal fixedpoints of logic programs

1985
*
Theoretical Computer Science
*

Furthermore

doi:10.1016/0304-3975(85)90128-8
fatcat:epdeqsld2nd7zn5qloyx53ozqm
*the*optimal fixedpoint*semantics*is consistent with Van Emden and Kowalski's*semantics**of**logic**programs*. ... In*the*context*of**logic**programming*we show that*the*optimal fixedpoint is equal to*the*least fixedpoint and is computable. ...*The*following theorem demonstrates that*the**semantics*we give to*logic**programs*is*equivalent*to*the**semantics**of*Van Emden and Kowalski. ...##
###
Semantic Versioning Checking in a Declarative Package Manager

2018
*
International Conference on Logic Programming
*

We extend a package manager for

doi:10.4230/oasics.iclp.2017.6
dblp:conf/iclp/Hanus17
fatcat:pvseesywnje5pdu4vxal3uapby
*the*functional*logic*language Curry with features to check*the**semantic**equivalence**of*two different versions*of*a software package. ... For this purpose, we combine CurryCheck, a tool for automated property testing, with*program*analysis techniques in order to ensure*the*termination*of**the*checker even in case*of*possibly non-terminating ... http://www.semver.org © Michael Hanus; licensed*under*Creative Commons License CC-BY This property is a necessary but not sufficient condition to ensure*semantic**equivalence*in functional*logic**programs*...##
###
Infinitary equilibrium logic and strongly equivalent logic programs

2017
*
Artificial Intelligence
*

We extend this line

doi:10.1016/j.artint.2017.02.002
fatcat:wbv5o7de5nfelin4fut7zrxdqm
*of*work to formulas with*infinitely*long conjunctions and disjunctions, show that*the*infinitary*logic**of*here-and-there characterizes*strong**equivalence**of*infinitary formulas, and ...*Strong**equivalence*is an important concept in*the*theory*of*answer set*programming*. Informally speaking, two sets*of*rules are strongly*equivalent*if they have*the*same meaning in any context. ...*The*first two authors were partially supported by*the*National Science Foundation*under*Grant IIS-1422455.*The*third author was partially supported by*the*projects TIN2013-42149-P and UPM RP151046021. ...##
###
Static Analysis, Abstract Interpretation and Verification in (Constraint Logic) Programming
[chapter]

2010
*
Lecture Notes in Computer Science
*

In [24] ,

doi:10.1007/978-3-642-14309-0_7
fatcat:pi5k44jpdfenzpf65lwfm3n5cm
*the*s-*semantics**of*constraint*logic**programs*is applied to symbolically reason on*infinite*-state transition systems. ... As shown in [24] ,*the*s-*semantics*for CLP can be used to extend*the*link between bottom-up evaluation*of**logic**programs*and model checking to*the*case*of**infinite*-state transition systems. ...
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