167 research outputs found
Space Efficiency of Propositional Knowledge Representation Formalisms
We investigate the space efficiency of a Propositional Knowledge
Representation (PKR) formalism. Intuitively, the space efficiency of a
formalism F in representing a certain piece of knowledge A, is the size of the
shortest formula of F that represents A. In this paper we assume that knowledge
is either a set of propositional interpretations (models) or a set of
propositional formulae (theorems). We provide a formal way of talking about the
relative ability of PKR formalisms to compactly represent a set of models or a
set of theorems. We introduce two new compactness measures, the corresponding
classes, and show that the relative space efficiency of a PKR formalism in
representing models/theorems is directly related to such classes. In
particular, we consider formalisms for nonmonotonic reasoning, such as
circumscription and default logic, as well as belief revision operators and the
stable model semantics for logic programs with negation. One interesting result
is that formalisms with the same time complexity do not necessarily belong to
the same space efficiency class
Compilability of Abduction
Abduction is one of the most important forms of reasoning; it has been
successfully applied to several practical problems such as diagnosis. In this
paper we investigate whether the computational complexity of abduction can be
reduced by an appropriate use of preprocessing. This is motivated by the fact
that part of the data of the problem (namely, the set of all possible
assumptions and the theory relating assumptions and manifestations) are often
known before the rest of the problem. In this paper, we show some complexity
results about abduction when compilation is allowed
Incrementally Computing Minimal Unsatisfiable Cores of QBFs via a Clause Group Solver API
We consider the incremental computation of minimal unsatisfiable cores (MUCs)
of QBFs. To this end, we equipped our incremental QBF solver DepQBF with a
novel API to allow for incremental solving based on clause groups. A clause
group is a set of clauses which is incrementally added to or removed from a
previously solved QBF. Our implementation of the novel API is related to
incremental SAT solving based on selector variables and assumptions. However,
the API entirely hides selector variables and assumptions from the user, which
facilitates the integration of DepQBF in other tools. We present implementation
details and, for the first time, report on experiments related to the
computation of MUCs of QBFs using DepQBF's novel clause group API.Comment: (fixed typo), camera-ready version, 6-page tool paper, to appear in
proceedings of SAT 2015, LNCS, Springe
Incremental QBF Solving
We consider the problem of incrementally solving a sequence of quantified
Boolean formulae (QBF). Incremental solving aims at using information learned
from one formula in the process of solving the next formulae in the sequence.
Based on a general overview of the problem and related challenges, we present
an approach to incremental QBF solving which is application-independent and
hence applicable to QBF encodings of arbitrary problems. We implemented this
approach in our incremental search-based QBF solver DepQBF and report on
implementation details. Experimental results illustrate the potential benefits
of incremental solving in QBF-based workflows.Comment: revision (camera-ready, to appear in the proceedings of CP 2014,
LNCS, Springer
Reduced Ordered Binary Decision Diagram with Implied Literals: A New knowledge Compilation Approach
Knowledge compilation is an approach to tackle the computational
intractability of general reasoning problems. According to this approach,
knowledge bases are converted off-line into a target compilation language which
is tractable for on-line querying. Reduced ordered binary decision diagram
(ROBDD) is one of the most influential target languages. We generalize ROBDD by
associating some implied literals in each node and the new language is called
reduced ordered binary decision diagram with implied literals (ROBDD-L). Then
we discuss a kind of subsets of ROBDD-L called ROBDD-i with precisely i implied
literals (0 \leq i \leq \infty). In particular, ROBDD-0 is isomorphic to ROBDD;
ROBDD-\infty requires that each node should be associated by the implied
literals as many as possible. We show that ROBDD-i has uniqueness over some
specific variables order, and ROBDD-\infty is the most succinct subset in
ROBDD-L and can meet most of the querying requirements involved in the
knowledge compilation map. Finally, we propose an ROBDD-i compilation algorithm
for any i and a ROBDD-\infty compilation algorithm. Based on them, we implement
a ROBDD-L package called BDDjLu and then get some conclusions from preliminary
experimental results: ROBDD-\infty is obviously smaller than ROBDD for all
benchmarks; ROBDD-\infty is smaller than the d-DNNF the benchmarks whose
compilation results are relatively small; it seems that it is better to
transform ROBDDs-\infty into FBDDs and ROBDDs rather than straight compile the
benchmarks.Comment: 18 pages, 13 figure
On the Complexity of Case-Based Planning
We analyze the computational complexity of problems related to case-based
planning: planning when a plan for a similar instance is known, and planning
from a library of plans. We prove that planning from a single case has the same
complexity than generative planning (i.e., planning "from scratch"); using an
extended definition of cases, complexity is reduced if the domain stored in the
case is similar to the one to search plans for. Planning from a library of
cases is shown to have the same complexity. In both cases, the complexity of
planning remains, in the worst case, PSPACE-complete
The DLV System for Knowledge Representation and Reasoning
This paper presents the DLV system, which is widely considered the
state-of-the-art implementation of disjunctive logic programming, and addresses
several aspects. As for problem solving, we provide a formal definition of its
kernel language, function-free disjunctive logic programs (also known as
disjunctive datalog), extended by weak constraints, which are a powerful tool
to express optimization problems. We then illustrate the usage of DLV as a tool
for knowledge representation and reasoning, describing a new declarative
programming methodology which allows one to encode complex problems (up to
-complete problems) in a declarative fashion. On the foundational
side, we provide a detailed analysis of the computational complexity of the
language of DLV, and by deriving new complexity results we chart a complete
picture of the complexity of this language and important fragments thereof.
Furthermore, we illustrate the general architecture of the DLV system which
has been influenced by these results. As for applications, we overview
application front-ends which have been developed on top of DLV to solve
specific knowledge representation tasks, and we briefly describe the main
international projects investigating the potential of the system for industrial
exploitation. Finally, we report about thorough experimentation and
benchmarking, which has been carried out to assess the efficiency of the
system. The experimental results confirm the solidity of DLV and highlight its
potential for emerging application areas like knowledge management and
information integration.Comment: 56 pages, 9 figures, 6 table
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