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A Trichotomy in the Complexity of Propositional Circumscription
[chapter]

2005
*
Lecture Notes in Computer Science
*

We prove that there exists a trichotomy for

doi:10.1007/978-3-540-32275-7_18
fatcat:wr4bfzscdzhtrl2j26jto2zadq
*the**complexity**of**the*inference problem in*propositional*variable*circumscription*. ...*The*inference problem for*propositional**circumscription*has been extensively studied from*the*viewpoint*of*computational*complexity*. ... Acknowledgments*The*author thanks Steffen Reith for providing*the*visualization*of*Post's lattice in Figure 1 . ...##
###
Page 3222 of Mathematical Reviews Vol. , Issue 98E
[page]

1998
*
Mathematical Reviews
*

expressiveness, showing that

*the*size*of**an**algebra*has nothing*to*do with its usefulness. ... in*complex*domains*of*knowledge. ...##
###
Page 1278 of Mathematical Reviews Vol. , Issue 2001B
[page]

2001
*
Mathematical Reviews
*

We use

*the*logical properties*of**circumscriptions*and cardinality-based*circumscriptions*in or- der*to*highlight*the*behavior*of*cardinality-based*circumscription*and*the*importance*of**the*fixed*propositions*... Summary: “*The*design*of*social laws for artificial agent societies is a basic*approach**to*coordinating multi-agent systems. ...##
###
The Complexity of Circumscriptive Inference in Post's Lattice
[chapter]

2009
*
Lecture Notes in Computer Science
*

In this paper, we study

doi:10.1007/978-3-642-04238-6_25
fatcat:nclnbcn5q5hanhknwawmkifzai
*the*computational*complexity**of*several formalizations*of*inference in*propositional**circumscription*for*the*case that*the*knowledge base is described by a*propositional*theory ... With its help, we determine*the**complexity**of**circumscriptive*inference for all but two possible classes*of*Boolean functions. ... He used this*approach**to*classify*the**complexity**of**the*satisfiability problem for all possible sets S. ...##
###
The Complexity of Circumscriptive Inference in Post's Lattice

2011
*
Theory of Computing Systems
*

In this paper, we study

doi:10.1007/s00224-010-9311-6
fatcat:dyjuk3c3kfbelpd5zhp2zoub3e
*the*computational*complexity**of*several formalizations*of*inference in*propositional**circumscription*for*the*case that*the*knowledge base is described by a*propositional*theory ... With its help, we determine*the**complexity**of**circumscriptive*inference for all but two possible classes*of*Boolean functions. ... He used this*approach**to*classify*the**complexity**of**the*satisfiability problem for all possible sets S. ...##
###
Page 2076 of Mathematical Reviews Vol. , Issue 98D
[page]

1998
*
Mathematical Reviews
*

Historically, many

*approaches**to*nonmonotonic reasoning, including default logic,*circumscription*, and autoepistemic logic, do not provide*an*ac- count*of*specificity, and so fail*to*enforce specificity ... For default logic*the*end result is a seminormal default theory; in*circumscription**the*end result is a set*of*abnormality*propositions*that, when circumscribed, yield a theory in which specificity information ...##
###
Page 6656 of Mathematical Reviews Vol. , Issue 90K
[page]

1990
*
Mathematical Reviews
*

Because

*of**the*high degree*of*abstraction, links*to*related mathe- matical topics in*algebra*, automata theory or category theory could be given. ... for testing*the*satisfiability*of**propositional*formulae. ...##
###
Page 1451 of Mathematical Reviews Vol. , Issue 2000b
[page]

2000
*
Mathematical Reviews
*

Our

*approach*is*to*solve*the*conflicts by giving*an*order*of*priority between*the*regulations*to*be merged. ... Using his program OTTER, McCune obtained*an*816-step proof that a certain set*of*10 equations is*an*axiomatization*of*Boolean*algebra*. ...##
###
Page 7077 of Mathematical Reviews Vol. , Issue 92m
[page]

1992
*
Mathematical Reviews
*

*of*great technical difficulty,

*the*field

*of*

*complex*nonlinear chaotic dynamics, and (3) it demonstrates

*the*power

*of*

*the*

*approach*by solving problems

*of*real interest

*to*working scientists and engineers ... 7077 ence or reasoning may be introduced as

*an*interpretation

*of*

*the*

*algebraic*considerations.” 92m:68109 68T20 Kosascxn, P. [Koval’ski, R.] ...

##
###
Page 1660 of Mathematical Reviews Vol. , Issue 94c
[page]

1994
*
Mathematical Reviews
*

Summary: “We present a new

*approach**to**the*problem*of**the*management*of**the*inconsistency in expert systems. ...*The*concept*of*a decomposition and recur- sive procedures based on relation theory and logical*algebra*are described. ...##
###
Page 3154 of Mathematical Reviews Vol. , Issue 90F
[page]

1990
*
Mathematical Reviews
*

Inspired by

*the*very good (linear)*complexity**of**propositional*Horn theories, we consider systems*of*Horn defaults. ... From*the*text: “We present*an**approach**to*formalizing*the*intuitive notion*of*a reasonable set*of*beliefs that on*the*one hand allows us*to*express a preference for one interpretation over another, thus ...##
###
Is intractability of nonmonotonic reasoning a real drawback?

1996
*
Artificial Intelligence
*

Some results about intractability

doi:10.1016/s0004-3702(96)00009-4
fatcat:crif2n3jwnbvvfhdbjrejymstq
*of**circumscription*and default logic can therefore be interpreted as*the*price one has*to*pay for having such*an*extra-compact representation. ... In particular, we prove that nonmonotonic formalisms such as*circumscription*and default logic allow for a much more compact and natural representation*of**propositional*knowledge than*propositional*calculus ... Acknowledgements*The*authors are grateful*to**the*anonymous referees for their comments and suggestions. ...##
###
Page 4358 of Mathematical Reviews Vol. , Issue 96g
[page]

1996
*
Mathematical Reviews
*

Summary: “We propose a technique for dealing with

*the*high*complexity**of*reasoning under*propositional*default logic and*circumscription*. ... This results in a new context-based*approach**to*default logic, called contex- tual default logic.*The**approach*extends*the*notion*of*a default rule and supplies each default extension with a context. ...##
###
Page 7075 of Mathematical Reviews Vol. , Issue 2003i
[page]

2003
*
Mathematical Reviews
*

*The*paper provides algorithms

*to*compute characteristic theorems, studies

*the*

*complexity*

*of*

*the*task, and discusses ways in which abduction,

*circumscription*, closed world assumption and some forms

*of*de ... Summary: “We present

*an*autoepistemic

*approach*for reasoning about actions in

*the*presence

*of*incomplete information and sens- ing. ...

##
###
Page 753 of Mathematical Reviews Vol. , Issue 99b
[page]

1991
*
Mathematical Reviews
*

*The*author proves that

*an*RFA, relativized functional

*algebra*, is isomorphic

*to*

*an*FLA, (full) functional lambda

*algebra*, by using a tool from nonstandard analysis, namely a comprehensive enlargement with ... in

*propositional*formalisms based on

*the*minimal knowledge paradigm, which is strictly related

*to*

*the*notion

*of*only knowing.” ...

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