2,003 research outputs found
Hybrid Rules with Well-Founded Semantics
A general framework is proposed for integration of rules and external first
order theories. It is based on the well-founded semantics of normal logic
programs and inspired by ideas of Constraint Logic Programming (CLP) and
constructive negation for logic programs. Hybrid rules are normal clauses
extended with constraints in the bodies; constraints are certain formulae in
the language of the external theory. A hybrid program is a pair of a set of
hybrid rules and an external theory. Instances of the framework are obtained by
specifying the class of external theories, and the class of constraints. An
example instance is integration of (non-disjunctive) Datalog with ontologies
formalized as description logics.
The paper defines a declarative semantics of hybrid programs and a
goal-driven formal operational semantics. The latter can be seen as a
generalization of SLS-resolution. It provides a basis for hybrid
implementations combining Prolog with constraint solvers. Soundness of the
operational semantics is proven. Sufficient conditions for decidability of the
declarative semantics, and for completeness of the operational semantics are
given
Sequentiality vs. Concurrency in Games and Logic
Connections between the sequentiality/concurrency distinction and the
semantics of proofs are investigated, with particular reference to games and
Linear Logic.Comment: 35 pages, appeared in Mathematical Structures in Computer Scienc
General Logic Programs as Infinite Games
In [vE86] M.H. van Emden introduced a simple game semantics for definite logic programs. Recently [RW05,GRW05], the authors extended this game to apply to logic programs with negation. Moreover, under the assumption that the programs have a finite number of rules, it was demonstrated in [RW05,GRW05] that the game is equivalent to the well-founded semantics of negation. In this paper we present work-in-progress towards demonstrating that the game of [RW05,GRW05] is equivalent to the well-founded semantics even in the case of programs that have a countably infinite number of rules. We argue however that in this case the proof of correctness has to be more involved. More specifically, in order to demonstrate that the game is correct one has to define a refined game in which each of the two players in his first move makes a bet in the form of a countable ordinal. Each ordinal can be considered as a kind of clock that imposes a "time limit" to the moves of the corresponding player. We argue that this refined game can be used to give the proof of correctness for the countably infinite case
On the equivalence between logic programming semantics and argumentation semantics
This work has been supported by the National Research Fund, Luxembourg (LAAMI project), by the Engineering and Physical Sciences Research Council (EPSRC, UK), grant Ref. EP/J012084/1 (SAsSy project), by CNPq (Universal 2012 – Proc. 473110/2012-1), and by CNPq/CAPES (Casadinho/PROCAD 2011).Peer reviewedPreprin
Exploiting Game Theory for Analysing Justifications
Justification theory is a unifying semantic framework. While it has its roots
in non-monotonic logics, it can be applied to various areas in computer
science, especially in explainable reasoning; its most central concept is a
justification: an explanation why a property holds (or does not hold) in a
model. In this paper, we continue the study of justification theory by means of
three major contributions. The first is studying the relation between
justification theory and game theory. We show that justification frameworks can
be seen as a special type of games. The established connection provides the
theoretical foundations for our next two contributions. The second contribution
is studying under which condition two different dialects of justification
theory (graphs as explanations vs trees as explanations) coincide. The third
contribution is establishing a precise criterion of when a semantics induced by
justification theory yields consistent results. In the past proving that such
semantics were consistent took cumbersome and elaborate proofs. We show that
these criteria are indeed satisfied for all common semantics of logic
programming. This paper is under consideration for acceptance in Theory and
Practice of Logic Programming (TPLP).Comment: Paper presented at the 36th International Conference on Logic
Programming (ICLP 2019), University Of Calabria, Rende (CS), Italy, September
2020, 15+8 page
Proving Correctness and Completeness of Normal Programs - a Declarative Approach
We advocate a declarative approach to proving properties of logic programs.
Total correctness can be separated into correctness, completeness and clean
termination; the latter includes non-floundering. Only clean termination
depends on the operational semantics, in particular on the selection rule. We
show how to deal with correctness and completeness in a declarative way,
treating programs only from the logical point of view. Specifications used in
this approach are interpretations (or theories). We point out that
specifications for correctness may differ from those for completeness, as
usually there are answers which are neither considered erroneous nor required
to be computed.
We present proof methods for correctness and completeness for definite
programs and generalize them to normal programs. For normal programs we use the
3-valued completion semantics; this is a standard semantics corresponding to
negation as finite failure. The proof methods employ solely the classical
2-valued logic. We use a 2-valued characterization of the 3-valued completion
semantics which may be of separate interest. The presented methods are compared
with an approach based on operational semantics. We also employ the ideas of
this work to generalize a known method of proving termination of normal
programs.Comment: To appear in Theory and Practice of Logic Programming (TPLP). 44
page
Defeasible Logic Programming: An Argumentative Approach
The work reported here introduces Defeasible Logic Programming (DeLP), a
formalism that combines results of Logic Programming and Defeasible
Argumentation. DeLP provides the possibility of representing information in the
form of weak rules in a declarative manner, and a defeasible argumentation
inference mechanism for warranting the entailed conclusions.
In DeLP an argumentation formalism will be used for deciding between
contradictory goals. Queries will be supported by arguments that could be
defeated by other arguments. A query q will succeed when there is an argument A
for q that is warranted, ie, the argument A that supports q is found undefeated
by a warrant procedure that implements a dialectical analysis.
The defeasible argumentation basis of DeLP allows to build applications that
deal with incomplete and contradictory information in dynamic domains. Thus,
the resulting approach is suitable for representing agent's knowledge and for
providing an argumentation based reasoning mechanism to agents.Comment: 43 pages, to appear in the journal "Theory and Practice of Logic
Programming
Datalog Queries Distributing over Components
We investigate the class D of queries that distribute over components. These are the queries that can be evaluated by taking the union of the query results over the connected components of the database instance. We show that it is undecidable whether a (positive) Datalog program distributes over components. Additionally, we show that connected Datalog ¬ (the fragment of Datalog ¬ where all rules are connected) provides an effective syntax for Datalog ¬ programs that distribute over components under the stratified as well as under the well-founded semantics. As a corollary, we obtain a simple proof for one of the main results in previous work [19], namely, that the classic win-move query is in F2 (a particular class of coordination-free queries)
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