7 research outputs found
SDDs are Exponentially More Succinct than OBDDs
Introduced by Darwiche (2011), sentential decision diagrams (SDDs) are
essentially as tractable as ordered binary decision diagrams (OBDDs), but tend
to be more succinct in practice. This makes SDDs a prominent representation
language, with many applications in artificial intelligence and knowledge
compilation. We prove that SDDs are more succinct than OBDDs also in theory, by
constructing a family of boolean functions where each member has polynomial SDD
size but exponential OBDD size. This exponential separation improves a
quasipolynomial separation recently established by Razgon (2013), and settles
an open problem in knowledge compilation
Knowledge Compilation of Logic Programs Using Approximation Fixpoint Theory
To appear in Theory and Practice of Logic Programming (TPLP), Proceedings of
ICLP 2015
Recent advances in knowledge compilation introduced techniques to compile
\emph{positive} logic programs into propositional logic, essentially exploiting
the constructive nature of the least fixpoint computation. This approach has
several advantages over existing approaches: it maintains logical equivalence,
does not require (expensive) loop-breaking preprocessing or the introduction of
auxiliary variables, and significantly outperforms existing algorithms.
Unfortunately, this technique is limited to \emph{negation-free} programs. In
this paper, we show how to extend it to general logic programs under the
well-founded semantics.
We develop our work in approximation fixpoint theory, an algebraical
framework that unifies semantics of different logics. As such, our algebraical
results are also applicable to autoepistemic logic, default logic and abstract
dialectical frameworks
On the relation between structured d-DNNFs and SDDs
Structured d-DNNFs and SDDs are restricted negation normal form circuits used in knowledge compilation as target languages into which propositional theories are compiled. Structuredness is imposed by so-called vtrees. By definition SDDs are restricted structured d-DNNFs. Beame and Liew (2015) as well as Bova and Szeider (2017) mentioned the question whether structured d-DNNFs are really more general than SDDs w.r.t. polynomial-size representations (w.r.t. the number of Boolean variables the represented functions are defined on.) The main result in the paper is the proof that a function can be represented by SDDs of polynomial size if the function and its complement have polynomial-size structured d-DNNFs that respect the same vtree
Three Modern Roles for Logic in AI
We consider three modern roles for logic in artificial intelligence, which
are based on the theory of tractable Boolean circuits: (1) logic as a basis for
computation, (2) logic for learning from a combination of data and knowledge,
and (3) logic for reasoning about the behavior of machine learning systems.Comment: To be published in PODS 202
On the role of canonicity in knowledge compilation
Knowledge compilation is a powerful reasoning paradigm with many applications across AI and computer science more broadly.
We consider the problem of bottom-up compilation of knowledge bases, which is usually predicated on the existence of a polytime function for combining compilations using Boolean operators (usually called an Apply function). While such a polytime Apply function is known to exist for certain languages (e.g., OBDDs) and not exist for others (e.g., DNNFs), its existence for certain languages remains unknown. Among the latter is the recently introduced language of Sentential Decision Diagrams (SDDs): while a polytime Apply function exists for SDDs, it was unknown whether such a function exists for the important subset of compressed SDDs which are canonical. We resolve this open question in this paper and consider some of its theoretical and practical implications. Some of the findings we report question the common wisdom on the relationship between bottom-up compilation, language canonicity and the complexity of the Apply function.acceptance rate of 26.67% for papers and 11.95% for oral presentationstatus: publishe