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34
Tractable reasoning in firstorder knowledge bases with disjunctive information
 In Proceedings of AAAI2005 and IAAI2005
, 2005
"... Abstract This work proposes a new methodology for establishing the tractability of a reasoning service that deals with expressive firstorder knowledge bases. It consists of defining a logic that is weaker than classical logic and that has two properties: first, the entailment problem can be reduce ..."
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Abstract This work proposes a new methodology for establishing the tractability of a reasoning service that deals with expressive firstorder knowledge bases. It consists of defining a logic that is weaker than classical logic and that has two properties: first, the entailment problem can be reduced to the model checking problem for a small number of characteristic models; and second, the model checking problem itself is tractable for formulas with a bounded number of variables. We show this methodology in action for the reasoning service previously proposed by Liu, Lakemeyer and Levesque for dealing with disjunctive information. They show that their reasoning is tractable in the propositional case and decidable in the firstorder case. Here we apply the methodology and prove that the reasoning is also tractable in the firstorder case if the knowledge base and the query both use a bounded number of variables.
Certain answers as objects and knowledge
 In KR
, 2014
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is retained by the author(s) and / or other copyright owners and it is a condition of accessing these publications that users recognise and abide by the legal requirements associated with these rights. Take down policy The University of Edinburgh has made every reasonable effort to ensure that Edinburgh Research Explorer content complies with UK legislation. If you believe that the public display of this file breaches copyright please contact openaccess@ed.ac.uk providing details, and we will remove access to the work immediately and investigate your claim.
Efficient Reasoning in Multiagent Epistemic Logics
"... Abstract. In many applications, agents must reason about what other agents know, whether to coordinate with them or to come out on top in a competitive situation. However in general, reasoning in a multiagent epistemic logic such as Kn has high complexity. In this paper, we look at a restricted clas ..."
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Abstract. In many applications, agents must reason about what other agents know, whether to coordinate with them or to come out on top in a competitive situation. However in general, reasoning in a multiagent epistemic logic such as Kn has high complexity. In this paper, we look at a restricted class of knowledge bases that are sets of modal literals. We call these proper epistemic knowledge bases (PEKBs). We show that after a PEKB has been put in prime implicate normal form (PINF), an efficient databaselike query evaluation procedure can be used to check whether an arbitrary query is entailed by the PEKB. The evaluation procedure is always sound and sometimes complete. We also develop a procedure to convert a PEKB into PINF. As well, we extend our approach to deal with introspection. 1
A Feasible Approach to Disjunctive Knowledge in Situation Calculus
, 2005
"... In this thesis we present LP, a reinterpretation of situation calculus based on intuitions from manyvalued logics. The key difference is that the notion of truth is based on the fact that a term is interpreted into a set of objects rather than one single object and equality is interpreted as “possi ..."
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In this thesis we present LP, a reinterpretation of situation calculus based on intuitions from manyvalued logics. The key difference is that the notion of truth is based on the fact that a term is interpreted into a set of objects rather than one single object and equality is interpreted as “possibly equals”. LP is suitable for defining action theories that capture fluentbased disjunctive knowledge, which means that any incomplete knowledge the theory captures is limited to be about the value of one fluent each time. This essentially enforces an independence assumption on the fluents which allows for efficient evaluation mechanisms. We show that like situation calculus a similar regression theorem holds in LP. Furthermore, we prove that LP can be embedded in situation calculus and show how a special form of LP theories can be soundly implemented in Prolog and the agent programming language Indigolog.
The Hyper System: Knowledge Reformation for Efficient Firstorder Hypothetical Reasoning
 In PRICAI’00, 6th Pacific Rim Int. Conf. on Artificial Intelligence
, 2000
"... . We present the Hyper system that implements a new approach to knowledge compilation, where functionfree firstorder acyclic Horn theories are transformed to propositional logic. The compilation method integrates techniques from deductive databases (relevance reasoning) and theory transformati ..."
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. We present the Hyper system that implements a new approach to knowledge compilation, where functionfree firstorder acyclic Horn theories are transformed to propositional logic. The compilation method integrates techniques from deductive databases (relevance reasoning) and theory transformation via unfold/fold transformations, to obtain a compact propositional representation. The transformed theory is more compact than the ground version of the original theory in terms of significantly less and mostly shorter clauses. This form of compilation, called knowledge (base) reformation, is important since the most efficient reasoning methods are defined for propositional theories, while knowledge is most naturally expressed in a firstorder language. In particular, we will show that knowledge reformation allows loworder polynomial time inference to find a nearoptimal solution in costbased firstorder hypothetical reasoning (or `abduction') problems. We will also present ex...
TWO APPROACHES TO EFFICIENT OPENWORLD REASONING
, 2000
"... We show how a simple but e cient evaluation procedure that is logically correct only for closedworld knowledge bases can nonetheless be used in certain contexts with openworld ones. We discuss two cases, one based on restricting queries to be in a certain normal form, and the other, arising in r ..."
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We show how a simple but e cient evaluation procedure that is logically correct only for closedworld knowledge bases can nonetheless be used in certain contexts with openworld ones. We discuss two cases, one based on restricting queries to be in a certain normal form, and the other, arising in reasoning about actions, based on having sensing information at the right time so as to dynamically reduce openword reasoning to closedword reasoning.
On the expressiveness of Levesque’s normal form
 J. Artif. Intell. Res. (JAIR
"... Levesque proposed a generalization of a database called a proper knowledge base (KB), which is equivalent to a possibly infinite consistent set of ground literals. In contrast to databases, proper KBs do not make the closedworld assumption and hence the entailment problem becomes undecidable. Leves ..."
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Levesque proposed a generalization of a database called a proper knowledge base (KB), which is equivalent to a possibly infinite consistent set of ground literals. In contrast to databases, proper KBs do not make the closedworld assumption and hence the entailment problem becomes undecidable. Levesque then proposed a limited but efficient inference method V for proper KBs, which is sound and, when the query is in a certain normal form, also logically complete. He conjectured that for every firstorder query there is an equivalent one in normal form. In this note, we show that this conjecture is false. In fact, we show that any class of formulas for which V is complete must be strictly less expressive than full firstorder logic. Moreover, in the propositional case it is very unlikely that a formula always has a polynomialsize normal form. 1.
Towards an Expressive Practical Logical Action Theory
"... In the area of reasoning about actions, one of the key computational problems is the projection problem: to find whether a given logical formula is true after performing a sequence of actions. This problem is undecidable in the general situation calculus; however, it is decidable in some fragments. ..."
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In the area of reasoning about actions, one of the key computational problems is the projection problem: to find whether a given logical formula is true after performing a sequence of actions. This problem is undecidable in the general situation calculus; however, it is decidable in some fragments. We consider a fragment P of the situation calculus and Reiter’s basic action theories (BAT) such that the projection problem can be reduced to the satisfiability problem in an expressive description logic ALCO(U) that includes nominals (O), the universal role (U), and constructs from the wellknown logic ALC. It turns out that our fragment P is more expressive than previously explored description logic based fragments of the situation calculus. We explore some of the logical properties of our theories. In particular, we show that the projection problem can be solved using regression in the case where BATs include a general “static ” TBox, i.e., an ontology that has no occurrences of fluents. Thus, we propose seamless integration of traditional ontologies with reasoning about actions. We also show that the projection problem can be solved using progression if all actions have only local effects on the fluents, i.e., in P, if one starts with an incomplete initial theory that can be transformed into an ALCO(U) concept, then its progression resulting from execution of a ground action can still be expressed in the same language. Moreover, we show that for a broad class of incomplete initial theories progression can be computed efficiently. 1
Model Expansion and the Expressiveness of FO(ID) and Other Logics
"... Model expansion problem is a question of determining, given a formula and a structure for a part of the vocabulary of the formula, whether there is an expansion of this structure that satisfies the formula. Recent development of a problemsolving paradigm based on model expansion by (Mitchell & ..."
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Model expansion problem is a question of determining, given a formula and a structure for a part of the vocabulary of the formula, whether there is an expansion of this structure that satisfies the formula. Recent development of a problemsolving paradigm based on model expansion by (Mitchell & Ternovska, 2005; Mitchell, Ternovska, Hach, & Mohebali, 2006) posed the question of complexity of this problem for logics used in the paradigm. We discuss the complexity of the model expansion problem for a number of logics, alongside that of satisfiability and model checking. As the task is equivalent to witnessing leading existential secondorder quantifiers in a model checking setting, the paper is in large part a survey of this area together with some new results. In particular, we describe the combined and data complexity of model expansion for FO(ID) (Denecker & Ternovska, 2008), as well as guarded and kguarded logics of (Andréka, van Benthem, & Németi, 1998) and (Gottlob, Leone, & Scarcello, 2001).
Propositional Independence  Conditional independence
, 2000
"... Independence – the study of what is relevant to a given problem of reasoning – is an important AI topic. In this paper, we investigate several notions of conditional independence in propositional logic: Darwiche and Pearl’s conditional independence, and two more restricted forms of it, called strong ..."
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Independence – the study of what is relevant to a given problem of reasoning – is an important AI topic. In this paper, we investigate several notions of conditional independence in propositional logic: Darwiche and Pearl’s conditional independence, and two more restricted forms of it, called strong conditional independence and perfect conditional independence. Many characterizations and properties of these independence relations are provided. We show them related to many other notions of independence pointed out so far in the literature (mainly formulavariable independence, irrelevance and novelty under various forms, separability, interactivity). We identify the computational complexity of conditional independence and of all these related independence relations.