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 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 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 Deriving conclusions from non-monotonic cause-effect relations

2016 ◽  
Vol 16 (5-6) ◽  
pp. 670-687 ◽  
Author(s):  
JORGE FANDINNO
Keyword(s):  
Knowledge Representation ◽  
Logic Programming ◽  
Causal Effect ◽  
Stable Model ◽  
Logic Programs ◽  
Causal Relations ◽  
Initial Approach ◽  
Sufficient Cause ◽  
Different Types ◽  
Normal Logic

AbstractWe present an extension of Logic Programming (under stable models semantics) that, not only allows concluding whether a true atom is a cause of another atom, but alsoderiving new conclusionsfrom these causal-effect relations. This is expressive enough to capture informal rules like “if some agent's actionshave beennecessaryto cause an eventEthen conclude atomcaused(,E),” something that, to the best of our knowledge, had not been formalised in the literature. To this aim, we start from a first attempt that proposed extending the syntax of logic programs with so-calledcausal literals. These causal literals are expressions that can be used in rule bodies and allow inspecting the derivation of some atomAin the program with respect to some query function ψ. Depending on how these query functions are defined, we can model different types of causal relations such as sufficient, necessary or contributory causes, for instance. The initial approach was specifically focused on monotonic query functions. This was enough to cover sufficient cause-effect relations but, unfortunately, necessary and contributory are essentiallynon-monotonic. In this work, we define a semantics for non-monotonic causal literals showing that, not only extends the stable model semantics for normal logic programs, but also preserves many of its usual desirable properties for the extended syntax. Using this new semantics, we provide precise definitions ofnecessaryandcontributorycausal relations and briefly explain their behaviour on a pair of typical examples from the Knowledge Representation literature.

scholarly journals Logic programs with monotone abstract constraint atoms

2008 ◽  
Vol 8 (2) ◽  
pp. 167-199 ◽  
Author(s):  
VICTOR W. MAREK ◽  
ILKKA NIEMELÄ ◽  
MIROSŁAW TRUSZCZYŃSKI
Keyword(s):  
Logic Programming ◽  
Logic Programs ◽  
Common Generalization ◽  
One Step ◽  
Normal Logic ◽  
The One ◽  
Operational Concept ◽  
Stable Models

AbstractWe introduce and study logic programs whose clauses are built out of monotone constraint atoms. We show that the operational concept of the one-step provability operator generalizes to programs with monotone constraint atoms, but the generalization involves nondeterminism. Our main results demonstrate that our formalism is a common generalization of (1) normal logic programming with its semantics of models, supported models and stable models, (2) logic programming with weight atoms lparse programs) with the semantics of stable models, as defined by Niemelä, Simons and Soininen, and (3) of disjunctive logic programming with the possible-model semantics of Sakama and Inoue.

scholarly journals On the Equivalence between Assumption-Based Argumentation and Logic Programming

2017 ◽  
Vol 60 ◽  
pp. 779-825 ◽  
Author(s):  
Martin Caminada ◽  
Claudia Schulz
Keyword(s):  
Logic Programming ◽  
Logic Program ◽  
The Other ◽  
Logic Programs ◽  
Special Cases ◽  
Reverse Translation ◽  
Normal Logic ◽  
The Relationship

Assumption-Based Argumentation (ABA) has been shown to subsume various other non-monotonic reasoning formalisms, among them normal logic programming (LP). We re-examine the relationship between ABA and LP and show that normal LP also subsumes (flat) ABA. More precisely, we specify a procedure that given a (flat) ABA framework yields an associated logic program with almost the same syntax whose semantics coincide with those of the ABA framework. That is, the 3-valued stable (respectively well-founded, regular, 2-valued stable, and ideal) models of the associated logic program coincide with the complete (respectively grounded, preferred, stable, and ideal) assumption labellings and extensions of the ABA framework. Moreover, we show how our results on the translation from ABA to LP can be reapplied for a reverse translation from LP to ABA, and observe that some of the existing results in the literature are in fact special cases of our work. Overall, we show that (flat) ABA frameworks can be seen as normal logic programs with a slightly different syntax. This implies that methods developed for one of these formalisms can be equivalently applied to the other by simply modifying the syntax.

scholarly journals Relating Multi-Adjoint Normal Logic Programs to Core Fuzzy Answer Set Programs from a Semantical Approach

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 881
Author(s):  
M. Eugenia Cornejo ◽  
David Lobo ◽  
Jesús Medina
Keyword(s):  
Fuzzy Logic ◽  
Logic Programming ◽  
Programming Language ◽  
Answer Set Programming ◽  
Logic Programs ◽  
The Core ◽  
Normal Logic ◽  
Answer Sets ◽  
Stable Models ◽  
Answer Set

This paper relates two interesting paradigms in fuzzy logic programming from a semantical approach: core fuzzy answer set programming and multi-adjoint normal logic programming. Specifically, it is shown how core fuzzy answer set programs can be translated into multi-adjoint normal logic programs and vice versa, preserving the semantics of the starting program. This translation allows us to combine the expressiveness of multi-adjoint normal logic programming with the compactness and simplicity of the core fuzzy answer set programming language. As a consequence, theoretical properties and results which relate the answer sets to the stable models of the respective logic programming frameworks are obtained. Among others, this study enables the application of the existence theorem of stable models developed for multi-adjoint normal logic programs to ensure the existence of answer sets in core fuzzy answer set programs.

LOGIC PROGRAMMING AND DEFAULT LOGIC

1994 ◽  
Vol 03 (03) ◽  
pp. 367-373
Author(s):  
GRIGORIS ANTONIOU
Keyword(s):  
Logic Programming ◽  
Ad Hoc ◽  
Logic Program ◽  
Operational Semantics ◽  
Main Property ◽  
Default Logic ◽  
Logic Programs ◽  
Default Theory ◽  
Normal Logic ◽  
Direct Use

We present several ideas of increasing complexity how to translate default theories to normal logic programs that make direct use of the deductive capacity of logic programming. We show the limitations of simple, ad hoc approaches, and arrive at a more general construction; its main property is that the answer substitutions computed by the logic program via its standard operational semantics correspond exactly to the extensions of the default theory.

A Modal Semantics of Negation in Logic Programming

1992 ◽  
Vol 16 (3-4) ◽  
pp. 231-262
Author(s):  
Philippe Balbiani
Keyword(s):  
Modal Logic ◽  
Logic Programming ◽  
Modal Logics ◽  
Kripke Models ◽  
Logic Programs ◽  
Modal Semantics ◽  
Soundness And Completeness ◽  
Modal Completion ◽  
Well Foundedness

The beauty of modal logics and their interest lie in their ability to represent such different intensional concepts as knowledge, time, obligation, provability in arithmetic, … according to the properties satisfied by the accessibility relations of their Kripke models (transitivity, reflexivity, symmetry, well-foundedness, …). The purpose of this paper is to study the ability of modal logics to represent the concepts of provability and unprovability in logic programming. The use of modal logic to study the semantics of logic programming with negation is defended with the help of a modal completion formula. This formula is a modal translation of Clack’s formula. It gives soundness and completeness proofs for the negation as failure rule. It offers a formal characterization of unprovability in logic programs. It characterizes as well its stratified semantics.

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