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Complete logic programs with domain-closure axiom

Paolo Mancarella, Simone Martini, Dino Pedreschi
1988 The Journal of Logic Programming  
Complete logic programs augmented with the domain-closure axiom are proposed as the reference theory for logic programming with negation as failure.  ...  Thus the notion of completion of a logic program, or complete logic program, was introduced, which consists of a simple transformation of a logic program P.  ...  D Complete logic programs augmented with the domain-closure axiom are proposed as the reference theory for logic programming with negation as failure.  ... 
doi:10.1016/0743-1066(88)90013-1 fatcat:l7w655e4xfcbha7avrt2ltknsy

Commonsense axiomatizations for logic programs

Allen Van Gelder, John S. Schlipf
1993 The Journal of Logic Programming  
D Various semantics for logic programs with negation are described in terms of a dualized program together with additional axioms, some of which are second-order formulas.  ...  The roles of domain augmentation and domain closure are examined. A "domain foundation" axiom is proposed to replace the domain closure axiom. a  ...  This attempt to express logic programming semantics in terms of classical logic was motivated by Robert Kowalski's expressed reservations about nonstandard logics and procedural definitions.  ... 
doi:10.1016/0743-1066(93)90030-k fatcat:y4d3faw765glhjnfzjeue2j77m

A logical framework for depiction and image interpretation

Raymond Reiter, Alan K. Mackworth
1989 Artificial Intelligence  
a reconstructton tn first-order logw of a stmphfied map-understanding program, Mapsee.  ...  We propose a logtcal framework for deptctton and mterpretatton that formahzes tmage domain knowledge, scene domain knowledge and the deptctton mapping between the tmage and scene domains Thts framework  ...  ACKNOWLEDGMENT We gratefully acknowledge several important discussions with Jan Mulder and Bill Havens and substantive critiques of earher versions of the paper by Wolfgang Blbel, Ted Elcock, Paul Gilmore  ... 
doi:10.1016/0004-3702(89)90008-8 fatcat:3b7mylpikvahvbza4dmpndfv6a

Algebras of modal operators and partial correctness

Bernhard Möller, Georg Struth
2006 Theoretical Computer Science  
This claim is supported by novel algebraic soundness and completeness proofs for Hoare logic and by connecting this formalism with an algebraic decision procedure.  ...  We study their properties in the associated operator algebras and show that the axioms of relation algebra are theorems at the operator level.  ...  Modal Kleene algebra also subsumes Hoare logic for programs with bounded non-determinism.  ... 
doi:10.1016/j.tcs.2005.09.069 fatcat:33kkwyysfjfb3fyp64qoh4anpy

Page 4098 of Mathematical Reviews Vol. , Issue 94g [page]

1994 Mathematical Reviews  
The roles of domain augmentation and domain closure are examined. A ‘do- main foundation’ axiom is proposed to replace the domain closure axiom.” 949:68024 68N17 68P20 Wood, Peter T.  ...  Summary: “Various semantics for logic programs with negation are described in terms of a dualized program together with additional axioms, some of which are second-order formulas.  ... 

Page 263 of Mathematical Reviews Vol. , Issue 85a [page]

1985 Mathematical Reviews  
In the general part we give a complete proof system for first-order temporal logic with detailed proofs of useful theorems. This logic enables reasoning about gen- eral time sequences.  ...  The domain-dependent part characterizes the special properties of the domain over which the program operates.  ... 

Combining Event Calculus and Description Logic Reasoning via Logic Programming [chapter]

Peter Baumgartner
2021 Lecture Notes in Computer Science  
The approach is exemplified with the logic programming language as implemented in the Fusemate system.  ...  The paper introduces a knowledge representation language that combines the event calculus with description logic in a logic programming framework.  ...  We start with a definition for the possible models splitting operator in terms of closures. Definition 1 (Split program closure). Let be a program and cl( ) its full closure.  ... 
doi:10.1007/978-3-030-86205-3_6 fatcat:wqqovl6xkjhkjfslt34hqcyt2m

Negation in logic programming

Kenneth Kunen
1987 The Journal of Logic Programming  
D We define a semantics for negation as failure in logic programming. Our semantics may be viewed as a cross between the approaches of Clark [5] and Fitting [7].  ...  As does [7], our semantics corresponds well with real PROLOG in the standard examples used in the literature to illustrate problems with [5] .  ...  This extension is obtained by following Kleene's truth tables for 3-valued logic; in line with the domain closure axiom (see Section 4) we are considering our domhn of discourse to be just the Herbrand  ... 
doi:10.1016/0743-1066(87)90007-0 fatcat:5vn5hj27hradncqhc3y4g6gq6y

Logic and Databases: A Deductive Approach

Herve Gallaire, Jack Minker, Jean-Marie Nicolas
1984 ACM Computing Surveys  
The purpose of this paper is to show that logic provides a convenient formalism for studying classical database problems.  ...  The second part deals mainly with the representation and manipulation of deduced facts and incomplete information.  ...  ACKNOWLEDGMENTS We thank Bob Kowalski and Ray Reiter, whose work in the field of logic and databases has been very influential, and for the many discussions that we have had with them over the past several  ... 
doi:10.1145/356924.356929 fatcat:ecummytddreebcif2pnfzp4td4

Logic and Databases: A Deductive Approach [chapter]

HERVÉ GALLAIRE, JACK MINKER, JEAN-MARIE NICOLAS
1989 Readings in Artificial Intelligence and Databases  
The purpose of this paper is to show that logic provides a convenient formalism for studying classical database problems.  ...  The second part deals mainly with the representation and manipulation of deduced facts and incomplete information.  ...  ACKNOWLEDGMENTS We thank Bob Kowalski and Ray Reiter, whose work in the field of logic and databases has been very influential, and for the many discussions that we have had with them over the past several  ... 
doi:10.1016/b978-0-934613-53-8.50020-0 fatcat:3jx23cl5czbclooawzwnzckxey

Situation calculus specifications for event calculus logic programs [chapter]

Rob Miller
1995 Lecture Notes in Computer Science  
A translation of Situation Calculus style theories into Event Calculus style logic programs is defined, and results are given on its soundness and completeness.  ...  A version of the Situation Calculus is presented which is able to deal with information about the actual occurrence of actions in time.  ...  Am] and a domain closure axiom for fluents f=F 1 v .... v f=F n v f=Neg(Fl) v .... v f=Neg(Fn )Although domain constraints have not been explicitly included in narrative domain descriptions, care must  ... 
doi:10.1007/3-540-59487-6_16 fatcat:jknatas3srd4dfmjfta64vl2uy

A note on the Declarative reading(s) of Logic Programming [article]

Marc Denecker
2000 arXiv   pre-print
This paper analyses the declarative readings of logic programming. Logic programming - and negation as failure - has no unique declarative reading.  ...  One common view is that logic programming is a logic for default reasoning, a sub-formalism of default logic or autoepistemic logic. In this view, negation as failure is a modal operator.  ...  This principle relies on the ability of the expert to interpret a logical axiom as a clear and precise statement about the domain of discourse.  ... 
arXiv:cs/0003056v1 fatcat:r3ihirojojfcvpfsibut2n3brm

Computational Adequacy in an Elementary Topos [chapter]

Alex K. Simpson
1999 Lecture Notes in Computer Science  
We place simple axioms on an elementary topos which sufce for it to provide a denotational model of call-by-value PCF with sum and product types.  ...  The main result characterises when the model is computationally adequate with respect to the operational semantics of the programming language.  ...  Acknowledgements This paper was written during a visit to Utrecht University supported by the NWO Pionier Project The Geometry of Logic led by Ieke Moerdijk.  ... 
doi:10.1007/10703163_22 fatcat:spvqgnmn6nfjll5stskvx7dpxy

Extending Classical Logic with Inductive Definitions [article]

Marc Denecker
2000 arXiv   pre-print
The goal of this paper is to extend classical logic with a generalized notion of inductive definition supporting positive and negative induction, to investigate the properties of this logic, its relationships  ...  to other logics in the area of non-monotonic reasoning, logic programming and deductive databases, and to show its application for knowledge representation by giving a typology of definitional knowledge  ...  Acknowledgements This work has benefitted from discussions with the following people: Maurice Bruynooghe, Danny Deschreye, Michael Gelfond, Vladimir Lifschitz, Victor Marek, Ray Reiter, Eugenia Ternovskaia  ... 
arXiv:cs/0003019v1 fatcat:svyilctko5hprckbrzjvpcc7ee

Shapiro Stewart. Second-order languages and mathematical practice. The journal of symbolic logic, vol. 50 (1985), pp. 714–742

Geoffrey Hellman
1989 Journal of Symbolic Logic (JSL)  
Indeed, if the semantics of Li contained only finite domains, then the respective logic would not be complete.  ...  I accept this because it is an application of the completeness axiom-an axiom that characterizes the real number structure".  ... 
doi:10.2307/2275038 fatcat:fej2qgprz5aebeaamucxxbylwy
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