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A Trichotomy in the Complexity of Propositional Circumscription [chapter]

Gustav Nordh
2005 Lecture Notes in Computer Science  
We prove that there exists a trichotomy for 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 .  ... 
doi:10.1007/978-3-540-32275-7_18 fatcat:wr4bfzscdzhtrl2j26jto2zadq

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]

Michael Thomas
2009 Lecture Notes in Computer Science  
In this paper, we study 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.  ... 
doi:10.1007/978-3-642-04238-6_25 fatcat:nclnbcn5q5hanhknwawmkifzai

The Complexity of Circumscriptive Inference in Post's Lattice

Michael Thomas
2011 Theory of Computing Systems  
In this paper, we study 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.  ... 
doi:10.1007/s00224-010-9311-6 fatcat:dyjuk3c3kfbelpd5zhp2zoub3e

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?

Marco Cadoli, Francesco M. Donini, Marco Schaerf
1996 Artificial Intelligence  
Some results about intractability 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.  ... 
doi:10.1016/s0004-3702(96)00009-4 fatcat:crif2n3jwnbvvfhdbjrejymstq

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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