52,773 research outputs found
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
A Relational Formulation of the Theory of Types
This paper developes a relational---as opposed to a functional---theory of types. The theory is based on Hilbert and Bernays' eta operator plus the identity symbol, from which Church's lambda and the other usual operators are then defined. The logic is intended for use in the semantics of natural language
Resumptions, Weak Bisimilarity and Big-Step Semantics for While with Interactive I/O: An Exercise in Mixed Induction-Coinduction
We look at the operational semantics of languages with interactive I/O
through the glasses of constructive type theory. Following on from our earlier
work on coinductive trace-based semantics for While, we define several big-step
semantics for While with interactive I/O, based on resumptions and
termination-sensitive weak bisimilarity. These require nesting inductive
definitions in coinductive definitions, which is interesting both
mathematically and from the point-of-view of implementation in a proof
assistant.
After first defining a basic semantics of statements in terms of resumptions
with explicit internal actions (delays), we introduce a semantics in terms of
delay-free resumptions that essentially removes finite sequences of delays on
the fly from those resumptions that are responsive. Finally, we also look at a
semantics in terms of delay-free resumptions supplemented with a silent
divergence option. This semantics hinges on decisions between convergence and
divergence and is only equivalent to the basic one classically.
We have fully formalized our development in Coq.Comment: In Proceedings SOS 2010, arXiv:1008.190
Properties of ABA+ for Non-Monotonic Reasoning
We investigate properties of ABA+, a formalism that extends the well studied
structured argumentation formalism Assumption-Based Argumentation (ABA) with a
preference handling mechanism. In particular, we establish desirable properties
that ABA+ semantics exhibit. These pave way to the satisfaction by ABA+ of some
(arguably) desirable principles of preference handling in argumentation and
nonmonotonic reasoning, as well as non-monotonic inference properties of ABA+
under various semantics.Comment: This is a revised version of the paper presented at the worksho
Formalising the pi-calculus using nominal logic
We formalise the pi-calculus using the nominal datatype package, based on
ideas from the nominal logic by Pitts et al., and demonstrate an implementation
in Isabelle/HOL. The purpose is to derive powerful induction rules for the
semantics in order to conduct machine checkable proofs, closely following the
intuitive arguments found in manual proofs. In this way we have covered many of
the standard theorems of bisimulation equivalence and congruence, both late and
early, and both strong and weak in a uniform manner. We thus provide one of the
most extensive formalisations of a process calculus ever done inside a theorem
prover.
A significant gain in our formulation is that agents are identified up to
alpha-equivalence, thereby greatly reducing the arguments about bound names.
This is a normal strategy for manual proofs about the pi-calculus, but that
kind of hand waving has previously been difficult to incorporate smoothly in an
interactive theorem prover. We show how the nominal logic formalism and its
support in Isabelle accomplishes this and thus significantly reduces the tedium
of conducting completely formal proofs. This improves on previous work using
weak higher order abstract syntax since we do not need extra assumptions to
filter out exotic terms and can keep all arguments within a familiar
first-order logic.Comment: 36 pages, 3 figure
Computing Preferred Answer Sets by Meta-Interpretation in Answer Set Programming
Most recently, Answer Set Programming (ASP) is attracting interest as a new
paradigm for problem solving. An important aspect which needs to be supported
is the handling of preferences between rules, for which several approaches have
been presented. In this paper, we consider the problem of implementing
preference handling approaches by means of meta-interpreters in Answer Set
Programming. In particular, we consider the preferred answer set approaches by
Brewka and Eiter, by Delgrande, Schaub and Tompits, and by Wang, Zhou and Lin.
We present suitable meta-interpreters for these semantics using DLV, which is
an efficient engine for ASP. Moreover, we also present a meta-interpreter for
the weakly preferred answer set approach by Brewka and Eiter, which uses the
weak constraint feature of DLV as a tool for expressing and solving an
underlying optimization problem. We also consider advanced meta-interpreters,
which make use of graph-based characterizations and often allow for more
efficient computations. Our approach shows the suitability of ASP in general
and of DLV in particular for fast prototyping. This can be fruitfully exploited
for experimenting with new languages and knowledge-representation formalisms.Comment: 34 pages, appeared as a Technical Report at KBS of the Vienna
University of Technology, see http://www.kr.tuwien.ac.at/research/reports
Minimal Negation in the Ternary Relational Semantics
Minimal Negation is defined within the basic positive relevance logic in the relational ternary semantics: B+. Thus, by defining a number of subminimal negations in the B+ context, principles of weak negation are shown to be isolable. Complete ternary semantics are offered for minimal negation in B+. Certain forms of reductio are conjectured to be undefinable (in ternary frames) without extending the positive logic. Complete semantics for such kinds of reductio in a properly extended positive logic are offered
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