1,375 research outputs found
Implementing Default and Autoepistemic Logics via the Logic of GK
The logic of knowledge and justified assumptions, also known as logic of
grounded knowledge (GK), was proposed by Lin and Shoham as a general logic for
nonmonotonic reasoning. To date, it has been used to embed in it default logic
(propositional case), autoepistemic logic, Turner's logic of universal
causation, and general logic programming under stable model semantics. Besides
showing the generality of GK as a logic for nonmonotonic reasoning, these
embeddings shed light on the relationships among these other logics. In this
paper, for the first time, we show how the logic of GK can be embedded into
disjunctive logic programming in a polynomial but non-modular translation with
new variables. The result can then be used to compute the extension/expansion
semantics of default logic, autoepistemic logic and Turner's logic of universal
causation by disjunctive ASP solvers such as claspD(-2), DLV, GNT and cmodels.Comment: Proceedings of the 15th International Workshop on Non-Monotonic
Reasoning (NMR 2014
Reasoning about Minimal Belief and Negation as Failure
We investigate the problem of reasoning in the propositional fragment of
MBNF, the logic of minimal belief and negation as failure introduced by
Lifschitz, which can be considered as a unifying framework for several
nonmonotonic formalisms, including default logic, autoepistemic logic,
circumscription, epistemic queries, and logic programming. We characterize the
complexity and provide algorithms for reasoning in propositional MBNF. In
particular, we show that entailment in propositional MBNF lies at the third
level of the polynomial hierarchy, hence it is harder than reasoning in all the
above mentioned propositional formalisms for nonmonotonic reasoning. We also
prove the exact correspondence between negation as failure in MBNF and negative
introspection in Moore's autoepistemic logic
Backdoors to Normality for Disjunctive Logic Programs
Over the last two decades, propositional satisfiability (SAT) has become one
of the most successful and widely applied techniques for the solution of
NP-complete problems. The aim of this paper is to investigate theoretically how
Sat can be utilized for the efficient solution of problems that are harder than
NP or co-NP. In particular, we consider the fundamental reasoning problems in
propositional disjunctive answer set programming (ASP), Brave Reasoning and
Skeptical Reasoning, which ask whether a given atom is contained in at least
one or in all answer sets, respectively. Both problems are located at the
second level of the Polynomial Hierarchy and thus assumed to be harder than NP
or co-NP. One cannot transform these two reasoning problems into SAT in
polynomial time, unless the Polynomial Hierarchy collapses. We show that
certain structural aspects of disjunctive logic programs can be utilized to
break through this complexity barrier, using new techniques from Parameterized
Complexity. In particular, we exhibit transformations from Brave and Skeptical
Reasoning to SAT that run in time O(2^k n^2) where k is a structural parameter
of the instance and n the input size. In other words, the reduction is
fixed-parameter tractable for parameter k. As the parameter k we take the size
of a smallest backdoor with respect to the class of normal (i.e.,
disjunction-free) programs. Such a backdoor is a set of atoms that when deleted
makes the program normal. In consequence, the combinatorial explosion, which is
expected when transforming a problem from the second level of the Polynomial
Hierarchy to the first level, can now be confined to the parameter k, while the
running time of the reduction is polynomial in the input size n, where the
order of the polynomial is independent of k.Comment: A short version will appear in the Proceedings of the Proceedings of
the 27th AAAI Conference on Artificial Intelligence (AAAI'13). A preliminary
version of the paper was presented on the workshop Answer Set Programming and
Other Computing Paradigms (ASPOCP 2012), 5th International Workshop,
September 4, 2012, Budapest, Hungar
A Multi-Engine Approach to Answer Set Programming
Answer Set Programming (ASP) is a truly-declarative programming paradigm
proposed in the area of non-monotonic reasoning and logic programming, that has
been recently employed in many applications. The development of efficient ASP
systems is, thus, crucial. Having in mind the task of improving the solving
methods for ASP, there are two usual ways to reach this goal: extending
state-of-the-art techniques and ASP solvers, or designing a new ASP
solver from scratch. An alternative to these trends is to build on top of
state-of-the-art solvers, and to apply machine learning techniques for choosing
automatically the "best" available solver on a per-instance basis.
In this paper we pursue this latter direction. We first define a set of
cheap-to-compute syntactic features that characterize several aspects of ASP
programs. Then, we apply classification methods that, given the features of the
instances in a {\sl training} set and the solvers' performance on these
instances, inductively learn algorithm selection strategies to be applied to a
{\sl test} set. We report the results of a number of experiments considering
solvers and different training and test sets of instances taken from the ones
submitted to the "System Track" of the 3rd ASP Competition. Our analysis shows
that, by applying machine learning techniques to ASP solving, it is possible to
obtain very robust performance: our approach can solve more instances compared
with any solver that entered the 3rd ASP Competition. (To appear in Theory and
Practice of Logic Programming (TPLP).)Comment: 26 pages, 8 figure
A Polynomial Translation of Logic Programs with Nested Expressions into Disjunctive Logic Programs: Preliminary Report
Nested logic programs have recently been introduced in order to allow for
arbitrarily nested formulas in the heads and the bodies of logic program rules
under the answer sets semantics. Nested expressions can be formed using
conjunction, disjunction, as well as the negation as failure operator in an
unrestricted fashion. This provides a very flexible and compact framework for
knowledge representation and reasoning. Previous results show that nested logic
programs can be transformed into standard (unnested) disjunctive logic programs
in an elementary way, applying the negation as failure operator to body
literals only. This is of great practical relevance since it allows us to
evaluate nested logic programs by means of off-the-shelf disjunctive logic
programming systems, like DLV. However, it turns out that this straightforward
transformation results in an exponential blow-up in the worst-case, despite the
fact that complexity results indicate that there is a polynomial translation
among both formalisms. In this paper, we take up this challenge and provide a
polynomial translation of logic programs with nested expressions into
disjunctive logic programs. Moreover, we show that this translation is modular
and (strongly) faithful. We have implemented both the straightforward as well
as our advanced transformation; the resulting compiler serves as a front-end to
DLV and is publicly available on the Web.Comment: 10 pages; published in Proceedings of the 9th International Workshop
on Non-Monotonic Reasonin
The Design of the Fifth Answer Set Programming Competition
Answer Set Programming (ASP) is a well-established paradigm of declarative
programming that has been developed in the field of logic programming and
nonmonotonic reasoning. Advances in ASP solving technology are customarily
assessed in competition events, as it happens for other closely-related
problem-solving technologies like SAT/SMT, QBF, Planning and Scheduling. ASP
Competitions are (usually) biennial events; however, the Fifth ASP Competition
departs from tradition, in order to join the FLoC Olympic Games at the Vienna
Summer of Logic 2014, which is expected to be the largest event in the history
of logic. This edition of the ASP Competition series is jointly organized by
the University of Calabria (Italy), the Aalto University (Finland), and the
University of Genova (Italy), and is affiliated with the 30th International
Conference on Logic Programming (ICLP 2014). It features a completely
re-designed setup, with novelties involving the design of tracks, the scoring
schema, and the adherence to a fixed modeling language in order to push the
adoption of the ASP-Core-2 standard. Benchmark domains are taken from past
editions, and best system packages submitted in 2013 are compared with new
versions and solvers.
To appear in Theory and Practice of Logic Programming (TPLP).Comment: 10 page
On Properties of Update Sequences Based on Causal Rejection
We consider an approach to update nonmonotonic knowledge bases represented as
extended logic programs under answer set semantics. New information is
incorporated into the current knowledge base subject to a causal rejection
principle enforcing that, in case of conflicts, more recent rules are preferred
and older rules are overridden. Such a rejection principle is also exploited in
other approaches to update logic programs, e.g., in dynamic logic programming
by Alferes et al. We give a thorough analysis of properties of our approach, to
get a better understanding of the causal rejection principle. We review
postulates for update and revision operators from the area of theory change and
nonmonotonic reasoning, and some new properties are considered as well. We then
consider refinements of our semantics which incorporate a notion of minimality
of change. As well, we investigate the relationship to other approaches,
showing that our approach is semantically equivalent to inheritance programs by
Buccafurri et al. and that it coincides with certain classes of dynamic logic
programs, for which we provide characterizations in terms of graph conditions.
Therefore, most of our results about properties of causal rejection principle
apply to these approaches as well. Finally, we deal with computational
complexity of our approach, and outline how the update semantics and its
refinements can be implemented on top of existing logic programming engines.Comment: 59 pages, 2 figures, 3 tables, to be published in "Theory and
Practice of Logic Programming
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