Syntax and semantics of multi-adjoint normal logic programming

2018 ◽  
Vol 345 ◽  
pp. 41-62 ◽  
Author(s):  
M. Eugenia Cornejo ◽  
David Lobo ◽  
Jesús Medina
Keyword(s):  
Logic Programming ◽  
Normal Logic

scholarly journals Interdefinability of defeasible logic and logic programming under the well-founded semantics

2011 ◽  
Vol 13 (1) ◽  
pp. 107-142 ◽  
Author(s):  
FREDERICK MAIER
Keyword(s):  
Logic Programming ◽  
Opposite Direction ◽  
Stable Model ◽  
Logic Programs ◽  
Defeasible Logic ◽  
Normal Logic

AbstractWe provide a method of translating theories of Nute's defeasible logic into logic programs, and a corresponding translation in the opposite direction. Under certain natural restrictions, the conclusions of defeasible theories under the ambiguity propagating defeasible logic ADL correspond to those of the well-founded semantics for normal logic programs, and so it turns out that the two formalisms are closely related. Using the same translation of logic programs into defeasible theories, the semantics for the ambiguity blocking defeasible logic NDL can be seen as indirectly providing an ambiguity blocking semantics for logic programs. We also provide antimonotone operators for both ADL and NDL, each based on the Gelfond–Lifschitz (GL) operator for logic programs. For defeasible theories without defeaters or priorities on rules, the operator for ADL corresponds to the GL operator and so can be seen as partially capturing the consequences according to ADL. Similarly, the operator for NDL captures the consequences according to NDL, though in this case no restrictions on theories apply. Both operators can be used to define stable model semantics for defeasible theories.

scholarly journals A Functorial Framework for Constraint Normal Logic Programming

2006 ◽  
pp. 555-577 ◽  
Author(s):  
Paqui Lucio ◽  
Fernando Orejas ◽  
Edelmira Pasarella ◽  
Elvira Pino
Keyword(s):  
Logic Programming ◽  
Normal Logic

scholarly journals Relating defeasible and normal logic programming through transformation properties

2003 ◽  
Vol 290 (1) ◽  
pp. 499-529 ◽  
Author(s):  
Carlos Iván Chesñevar ◽  
Jürgen Dix ◽  
Frieder Stolzenburg ◽  
G.R.Guillermo Ricardo Simari
Keyword(s):  
Logic Programming ◽  
Normal Logic

scholarly journals A Functorial Framework for Constraint Normal Logic Programming

2008 ◽  
Vol 16 (3) ◽  
pp. 421-450 ◽  
Author(s):  
P. Lucio ◽  
F. Orejas ◽  
E. Pasarella ◽  
E. Pino
Keyword(s):  
Logic Programming ◽  
Normal Logic

scholarly journals Default Negation as Explicit Negation plus Update

2021 ◽  
Vol 27 (1) ◽  
pp. 64-81
Author(s):  
Reinhard Kahle
Keyword(s):  
Logic Programming ◽  
Dynamic Logic ◽  
Stable Model ◽  
Normal Logic ◽  
Explicit Negation

 We argue that under the stable model semantics default negation can be read as explicit negation with update. We show that dynamic logic programming which is based on default negation, even in the heads, can be interpreted in a variant of updates with explicit negation only. As corollaries, we get an easy description of default negation in generalized and normal logic programming where initially negated literals are updated. These results are discussed with respect to the understanding of negation in logic.

scholarly journals Stable-unstable semantics: Beyond NP with normal logic programs

2016 ◽  
Vol 16 (5-6) ◽  
pp. 570-586 ◽  
Author(s):  
BART BOGAERTS ◽  
TOMI JANHUNEN ◽  
SHAHAB TASHARROFI
Keyword(s):  
Logic Programming ◽  
Logic Programs ◽  
New Paradigm ◽  
Search Problems ◽  
Quantified Boolean Formulas ◽  
Disjunctive Logic Programs ◽  
Boolean Formulas ◽  
Normal Logic ◽  
The Rich ◽  
High Level

AbstractStandard answer set programming (ASP) targets at solving search problems from the first level of the polynomial time hierarchy (PH). Tackling search problems beyond NP using ASP is less straightforward. The class of disjunctive logic programs offers the most prominent way of reaching the second level of the PH, but encoding respective hard problems as disjunctive programs typically requires sophisticated techniques such as saturation or meta-interpretation. The application of such techniques easily leads to encodings that are inaccessible to non-experts. Furthermore, while disjunctive ASP solvers often rely on calls to a (co-)NP oracle, it may be difficult to detect from the input program where the oracle is being accessed. In other formalisms, such as Quantified Boolean Formulas (QBFs), the interface to the underlying oracle is more transparent as it is explicitly recorded in the quantifier prefix of a formula. On the other hand, ASP has advantages over QBFs from the modeling perspective. The rich high-level languages such as ASP-Core-2 offer a wide variety of primitives that enable concise and natural encodings of search problems. In this paper, we present a novel logic programming–based modeling paradigm that combines the best features of ASP and QBFs. We develop so-calledcombined logic programsin which oracles are directly cast as (normal) logic programs themselves. Recursive incarnations of this construction enable logic programming on arbitrarily high levels of the PH. We develop a proof-of-concept implementation for our new paradigm.

scholarly journals Logical English meets legal English for swaps and derivatives

2021 ◽  
Author(s):  
Robert Kowalski ◽  
Akber Datoo
Keyword(s):  
Logic Programming ◽  
Standard Form ◽  
English Speakers ◽  
Logic Programs ◽  
Basic Form ◽  
Computer Languages ◽  
Legal Documents ◽  
Controlled Natural Language ◽  
Normal Logic ◽  
Conventional Computer

AbstractIn this paper, we present an informal introduction to Logical English (LE) and illustrate its use to standardise the legal wording of the Automatic Early Termination (AET) clauses of International Swaps and Derivatives Association (ISDA) Agreements. LE can be viewed both as an alternative to conventional legal English for expressing legal documents, and as an alternative to conventional computer languages for automating legal documents. LE is a controlled natural language (CNL), which is designed both to be computer-executable and to be readable by English speakers without special training. The basic form of LE is syntactic sugar for logic programs, in which all sentences have the same standard form, either as rules of the form conclusion if conditions or as unconditional sentences of the form conclusion. However, LE extends normal logic programming by introducing features that are present in other computer languages and other logics. These features include typed variables signalled by common nouns, and existentially quantified variables in the conclusions of sentences signalled by indefinite articles. Although LE translates naturally into a logic programming language such as Prolog or ASP, it can also serve as a neutral standard, which can be compiled into other lower-level computer languages.

scholarly journals Properties and Applications of Programs with Monotone and Convex Constraints

2006 ◽  
Vol 27 ◽  
pp. 299-334 ◽  
Author(s):  
L. Liu ◽  
M. Truszczynski
Keyword(s):  
Logic Programming ◽  
Program Completion ◽  
Convex Constraints ◽  
Normal Logic ◽  
Stable Models

We study properties of programs with monotone and convex constraints. We extend to these formalisms concepts and results from normal logic programming. They include the notions of strong and uniform equivalence with their characterizations, tight programs and Fages Lemma, program completion and loop formulas. Our results provide an abstract account of properties of some recent extensions of logic programming with aggregates, especially the formalism of lparse programs. They imply a method to compute stable models of lparse programs by means of off-the-shelf solvers of pseudo-boolean constraints, which is often much faster than the smodels system.

Reasoning about Dynamic Preferences in Circumscriptive Theory by Logic Programming

1997 ◽  
Vol 1 (2) ◽  
pp. 121-129 ◽  
Author(s):  
Toshiko Wakaki ◽  
◽  
Ken Satoh ◽  
Katsumi Nitta ◽  
◽  
...  
Keyword(s):  
Logic Programming ◽  
Logic Program ◽  
Legal Reasoning ◽  
Preference Information ◽  
Normal Logic ◽  
Object Level ◽  
Normal Logic Program ◽  
Dynamic Preferences

To treat dynamic preferences correctly is inevitably required in legal reasoning. In this paper, we present a method which enables us to handle some class of dynamic preferences in the framework of circumscription and to consistently compute its metalevel and object-level reasoning by expressing them in an extended logic program. This is achieved on the basis of policy axioms and priority axioms which permit as to describe circumscription policy by axioms and play a role in intervening between metalevel and object-level reasoning. Not only the preference information among rules and metarules but also relations between dynamic preferences and priority axioms in circumscription are represented by a normal logic program. Thus, priorities can be derived from the preferences dynamically, which allows us to compute objectlevel circumscriptive theory using logic programming based on Wakaki and Satoh’s method.

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