13 research outputs found
Externally Supported Models for Efficient Computation of Paracoherent Answer Sets
Answer Set Programming (ASP) is a well established formalism for nonmonotonic reasoning. While incoherence, the non-existence of answer sets for some programs, is an important feature of ASP, it has frequently been criticised and indeed has some disadvantages, especially for query answering. Paracoherent semantics have been suggested as a remedy, which extend the classical notion of answer sets to draw meaningful conclusions also from incoherent programs. In this paper we present an alternative characterization of the two major paracoherent semantics in terms of (extended) externally supported models. This definition uses a transformation of ASP programs that is more parsimonious than the classic epistemic transformation used in recent implementations. A performance comparison carried out on benchmarks from ASP competitions shows that the usage of the new transformation brings about performance improvements that are independent of the underlying algorithms
Modular Logic Programming: Full Compositionality and Conflict Handling for Practical Reasoning
With the recent development of a new ubiquitous nature of data and the profusity
of available knowledge, there is nowadays the need to reason from multiple sources
of often incomplete and uncertain knowledge. Our goal was to provide a way to
combine declarative knowledge bases – represented as logic programming modules
under the answer set semantics – as well as the individual results one already inferred
from them, without having to recalculate the results for their composition and without
having to explicitly know the original logic programming encodings that produced
such results. This posed us many challenges such as how to deal with fundamental
problems of modular frameworks for logic programming, namely how to define a
general compositional semantics that allows us to compose unrestricted modules.
Building upon existing logic programming approaches, we devised a framework
capable of composing generic logic programming modules while preserving the
crucial property of compositionality, which informally means that the combination of
models of individual modules are the models of the union of modules. We are also
still able to reason in the presence of knowledge containing incoherencies, which is
informally characterised by a logic program that does not have an answer set due
to cyclic dependencies of an atom from its default negation. In this thesis we also
discuss how the same approach can be extended to deal with probabilistic knowledge
in a modular and compositional way.
We depart from the Modular Logic Programming approach in Oikarinen &
Janhunen (2008); Janhunen et al. (2009) which achieved a restricted form of compositionality
of answer set programming modules. We aim at generalising this
framework of modular logic programming and start by lifting restrictive conditions
that were originally imposed, and use alternative ways of combining these (so called
by us) Generalised Modular Logic Programs. We then deal with conflicts arising
in generalised modular logic programming and provide modular justifications and
debugging for the generalised modular logic programming setting, where justification
models answer the question: Why is a given interpretation indeed an Answer Set?
and Debugging models answer the question: Why is a given interpretation not an
Answer Set?
In summary, our research deals with the problematic of formally devising a
generic modular logic programming framework, providing: operators for combining
arbitrary modular logic programs together with a compositional semantics; We
characterise conflicts that occur when composing access control policies, which are
generalisable to our context of generalised modular logic programming, and ways of
dealing with them syntactically: provided a unification for justification and debugging
of logic programs; and semantically: provide a new semantics capable of dealing
with incoherences. We also provide an extension of modular logic programming
to a probabilistic setting. These goals are already covered with published work. A prototypical tool implementing the unification of justifications and debugging is
available for download from http://cptkirk.sourceforge.net
On the Computation of Paracoherent Answer Sets
Answer Set Programming (ASP) is a well-established formalism for nonmonotonic
reasoning. An ASP program can have no answer set due to cyclic default
negation. In this case, it is not possible to draw any conclusion, even if this
is not intended. Recently, several paracoherent semantics have been proposed
that address this issue, and several potential applications for these semantics
have been identified. However, paracoherent semantics have essentially been
inapplicable in practice, due to the lack of efficient algorithms and
implementations. In this paper, this lack is addressed, and several different
algorithms to compute semi-stable and semi-equilibrium models are proposed and
implemented into an answer set solving framework. An empirical performance
comparison among the new algorithms on benchmarks from ASP competitions is
given as well
Minimal Undefinedness for Fuzzy Answer Sets
Fuzzy Answer Set Programming (FASP) combines the non-monotonic reasoning typical of Answer Set Programming with the capability of Fuzzy Logic to deal with imprecise information and paraconsistent reasoning. In the context of paraconsistent reasoning, the fundamental principle of minimal undefinedness states that truth degrees close to 0 and 1 should be preferred to those close to 0.5, to minimize the ambiguity of the scenario. The aim of this paper is to enforce such a principle in FASP through the minimization of a measure of undefinedness. Algorithms that minimize undefinedness of fuzzy answer sets are presented, and implemented
A Paraconsistent ASP-like Language with Tractable Model Generation
Answer Set Programming (ASP) is nowadays a dominant rule-based knowledge
representation tool. Though existing ASP variants enjoy efficient
implementations, generating an answer set remains intractable. The goal of this
research is to define a new \asp-like rule language, 4SP, with tractable model
generation. The language combines ideas of ASP and a paraconsistent rule
language 4QL. Though 4SP shares the syntax of \asp and for each program all its
answer sets are among 4SP models, the new language differs from ASP in its
logical foundations, the intended methodology of its use and complexity of
computing models.
As we show in the paper, 4QL can be seen as a paraconsistent counterpart of
ASP programs stratified with respect to default negation. Although model
generation of well-supported models for 4QL programs is tractable, dropping
stratification makes both 4QL and ASP intractable. To retain tractability while
allowing non-stratified programs, in 4SP we introduce trial expressions
interlacing programs with hypotheses as to the truth values of default
negations. This allows us to develop a~model generation algorithm with
deterministic polynomial time complexity.
We also show relationships among 4SP, ASP and 4QL
Abstract Argumentation and Answer Set Programming: Two Faces of Nelson’s Logic
In this work, we show that both logic programming and abstract argumentation frameworks can be interpreted in terms of Nelson’s constructive logic N4. We do so by formalising, in this logic, two principles that we call noncontradictory inference and strengthened closed world assumption: the first states that no belief can be held based on contradictory evidence while the latter forces both unknown and contradictory evidence to be regarded as false. Using these principles, both logic programming and abstract argumentation frameworks are translated into constructive logic in a modular way and using the object language. Logic programming implication and abstract argumentation supports become, in the translation, a new implication connective following the noncontradictory inference principle. Attacks are then represented by combining this new implication with strong negation. Under consideration in Theory and Practice of Logic Programming (TPLP)
Promoting Modular Nonmonotonic Logic Programs
Modularity in Logic Programming has gained much attention over the past years. To date, many formalisms have been proposed that feature various aspects of modularity. In this paper, we present our current work on Modular Nonmonotonic Logic Programs (MLPs), which are logic programs under answer set semantics with modules that have contextualized input provided by other modules. Moreover, they allow for (mutually) recursive module calls. We pinpoint issues that are present in such cyclic module systems and highlight how MLPs addresses them
Efficient paraconsistent reasoning with rules and ontologies for the semantic web
Ontologies formalized by means of Description Logics (DLs) and rules in the form of Logic Programs (LPs) are two prominent formalisms in the field of Knowledge Representation and Reasoning. While DLs adhere to the OpenWorld Assumption and are suited for taxonomic reasoning, LPs implement reasoning under the Closed World Assumption, so that default knowledge can be expressed. However, for many applications it is useful to have a means that allows reasoning over an open domain and expressing rules with exceptions at the same time. Hybrid MKNF knowledge bases make such a means available by formalizing DLs and LPs in a common logic, the Logic of Minimal Knowledge and Negation as Failure (MKNF).
Since rules and ontologies are used in open environments such as the Semantic Web,
inconsistencies cannot always be avoided. This poses a problem due to the Principle of Explosion, which holds in classical logics. Paraconsistent Logics offer a solution to this issue by assigning meaningful models even to contradictory sets of formulas. Consequently, paraconsistent semantics for DLs and LPs have been investigated intensively. Our goal is to apply the paraconsistent approach to the combination of DLs and LPs in hybrid MKNF knowledge bases.
In this thesis, a new six-valued semantics for hybrid MKNF knowledge bases is introduced, extending the three-valued approach by Knorr et al., which is based on the wellfounded semantics for logic programs. Additionally, a procedural way of computing paraconsistent well-founded models for hybrid MKNF knowledge bases by means of an alternating fixpoint construction is presented and it is proven that the algorithm is sound and complete w.r.t. the model-theoretic characterization of the semantics. Moreover, it is shown that the new semantics is faithful w.r.t. well-studied paraconsistent semantics for DLs and LPs, respectively, and maintains the efficiency of the approach it extends