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Page 4234 of Mathematical Reviews Vol. , Issue 81J
[page]

1981
*
Mathematical Reviews
*

*of*

*normal*

*forms*are stated

*and*this

*complexity*is maxi- mized, in some interesting cases, as a function

*of*parameters de- scribing

*the*sructures

*of*

*the*current

*normal*

*forms*.” 81j:68016 van Emde Boas, P ... Authors’ summary: “

*The*

*complexity*

*of*a A-term is defined as

*the*number

*of*B-reductions needed to reach its

*normal*

*form*. in

*the*present paper some general properties

*of*

*the*

*complexity*

*of*appli- cations ...

##
###
Page 7274 of Mathematical Reviews Vol. , Issue 98K
[page]

1998
*
Mathematical Reviews
*

We also show that under these conditions

*the*key*of*a relation is unique*and*a relation in third*normal**form*is also in Boyce-Codd*normal**form*. ... Summary: “This paper studies*the**complexity**of**the*query- answering problem in*logic*databases with*complex*values. ...##
###
Page 442 of Mathematical Reviews Vol. , Issue 91A
[page]

1991
*
Mathematical Reviews
*

*The*lengths

*of*

*computations*

*of*

*logic*

*programs*in

*normal*

*form*are studied. ... Summary: “It is shown that every pure

*logic*

*program*can be transformed to a

*normal*

*form*without changing

*the*lengths

*of*

*computations*

*and*

*the*data flow during

*computation*. ...

##
###
An overview of nonmonotonic reasoning and logic programming

1993
*
The Journal of Logic Programming
*

It is

doi:10.1016/0743-1066(93)90028-f
fatcat:zs5h4ximffdfvapevyr6rvs4fm
*of*interest to note that all three topics-nonmonotonic*logic*,*logic**programming*,*and**computational**complexity*-are unique contributions made to*logic*by*computer*scientists. ... This section is subdivided into several subsections, which deal with*the*following:*normal**and*extended*logic**programs*; disjunctive*logic**programs*; abductive*logic**programs*;*and**complexity**and*properties ...##
###
Page 6976 of Mathematical Reviews Vol. , Issue 96k
[page]

1996
*
Mathematical Reviews
*

to

*normal**logic**programs*. ... to*normal**logic**programs*. ...##
###
Reduction Strategies for Declarative Programming

2001
*
Electronical Notes in Theoretical Computer Science
*

On

doi:10.1016/s1571-0661(04)00273-7
fatcat:jtcnfes5ireuxlctdpm6nxkehm
*the*other hand, they should also support*the*programmers to write*programs*in a declarative way ignoring*the*influence*of**the*evaluation strategy to*the*success*of*a*computation*as good as possible. ... This paper surveys reduction or evaluation strategies for functional*and*functional*logic**programs*. ... Apart from these details, a reasonable reduction strategy to evaluate expressions should be*normalizing*, i.e., it should*compute*a*normal**form*w.r.t.*the*rewrite*logic*whenever it exists (without a termination ...##
###
The Use of Instrumental and Controlling Program Master of Logic for Solving the Basic Class Problems of Propositional Algebra: Didactic Aspect

2013
*
American Journal of Educational Research
*

*The*basic opportunities

*of*Master

*of*

*Logic*

*program*are considered in

*the*article. ...

*The*article is primarily assigned for Discrete Mathematics, Mathematical

*Logics*, Artificial Intelligence, etc. teachers

*of*higher schools,

*Computer*Science

*and*Mathematics teachers

*of*secondary schools ...

*The*universal method

*of*Quine-McCluskey adopted by

*the*author for

*computer*use is in

*the*basis

*of*building minimal

*normal*

*forms*mechanism being

*programmed*in Master

*of*

*Logic*(See e.g. ...

##
###
Page 1739 of Mathematical Reviews Vol. , Issue 95c
[page]

1995
*
Mathematical Reviews
*

To do so, we transform

*the**normal**programs*into disjunctive*logic**programs**and*sets*of*integrity constraints. ... These relations are then used to prove*the**computational**complexity**of*reasoning with*the*positivistic*and*minimally-supported model se- mantics, as well as new*complexity*results for restricted subsets ...##
###
Computability and logic

1990
*
Discrete Applied Mathematics
*

Diophantine sets

doi:10.1016/0166-218x(90)90034-a
fatcat:amvpt4fvfzau5epbhl7xp3zccm
*and*functions. Coding*computations*. diophantine predicates*and*Kleene's*Normal**Form*Theorem.*The*four squares theorem. 10: Indexings*and**the*Recursion Theorem. Pairings. Indexings. ... Godel's sequencing function*and*min-*computable*functions. Universal PART II:*LOGIC*. 11: Propositional*Logic*. Background.*The*language*of*propositional*logic*. Truth. Proof. Soundness. ...##
###
Forgetting under the Well-Founded Semantics
[chapter]

2013
*
Lecture Notes in Computer Science
*

In this paper, we develop a notion

doi:10.1007/978-3-642-40564-8_4
fatcat:li7ycn5duncy5hx2htugljyzt4
*of*forgetting for*normal**logic**programs*under*the*well-founded semantics. We show that a number*of*desirable properties are satisfied by our approach. ... Three different algorithms are presented that maintain*the**computational**complexity**of**the*well-founded semantics, while partly keeping its syntactical structure. ... Preliminaries A*normal**logic**program*P , or simply*logic**program*, is a finite set*of*rules r*of**the**form*h ← a 1 , . . . , a n , not b 1 , . . . , not b m where h, a i ,*and*b j , with 1 ≤ i ≤ n*and*1 ...##
###
Page 6362 of Mathematical Reviews Vol. , Issue 89K
[page]

1989
*
Mathematical Reviews
*

*The*paper discusses at an informal level

*the*implication

*of*

*the*

*computational*

*complexity*

*of*

*logic*to human

*and*artificial cogni- tion. ... A

*normal*

*form*is an expression that cannot be reduced;

*the*class

*of*sentences that are reduced to

*the*same

*normal*

*form*constitutes a semantic field

*of*sentences. ...

##
###
Bridging the Gap between Reinforcement Learning and Knowledge Representation: A Logical Off- and On-Policy Framework
[article]

2010
*
arXiv
*
pre-print

In this paper, we bridge

arXiv:1012.1552v1
fatcat:pqgnvdzv55gkxa6lyednmz57hu
*the*gap between reinforcement learning*and*knowledge representation, by providing a rich knowledge representation framework, based on*normal**logic**programs*with answer set semantics ... We prove*the*correctness*of*our approach. We show that*the**complexity**of*finding an offline*and*online policy for a model-free reinforcement learning problem in our approach is NP-complete. ... A Herbrand interpretation is a subset*of**the*Herbrand base . A*normal**logic**program*is a finite set*of*rules*of**the**form*Where are atoms*and*is*the*negation-as-failure. ...##
###
Cellular logic image processing

1990
*
Discrete Applied Mathematics
*

Diophantine sets

doi:10.1016/0166-218x(90)90035-b
fatcat:3mmrof7hrvepbckvqzghj5zrh4
*and*functions. Coding*computations*. diophantine predicates*and*Kleene's*Normal**Form*Theorem.*The*four squares theorem. 10: Indexings*and**the*Recursion Theorem. Pairings. Indexings. ... Godel's sequencing function*and*min-*computable*functions. Universal PART II:*LOGIC*. 11: Propositional*Logic*. Background.*The*language*of*propositional*logic*. Truth. Proof. Soundness. ...##
###
Page 476 of Mathematical Reviews Vol. , Issue 98A
[page]

1998
*
Mathematical Reviews
*

*The*purpose is to understand

*the*

*computational*

*complexity*

*of*these inference ... This makes it possible to evaluate in a uniform way

*the*de- gree

*of*unsolvability [|

*of*

*the*following two subclasses

*of*

*normal*

*logic*

*programs*: (i)

*the*set

*of*locally stratified

*programs*

*and*(ii)

*the*set ...

##
###
Enhancing Linear Algebraic Computation of Logic Programs Using Sparse Representation

2021
*
New generation computing
*

In this paper, we analyze

doi:10.1007/s00354-021-00142-2
fatcat:wok2i35albgvzcvuksjpoqkqhe
*the**complexity**of**the*linear algebraic methods for*logic**programs**and*propose further improvement by using sparse matrices to embed*logic**programs*in vector spaces. ... We also apply*the*method to*the**computation**of*stable models*of**normal**programs*, in which*the*guesses are associated with initial matrices,*and*verify its effect when there are small numbers*of*negation ... Taisuke Sato for his valuable comments*and*useful critiques*of*this research. This work has been supported in part by JSPS KAKENHI Grant Numbers 17H00763*and*18H03288. ...
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