108 research outputs found
Normal-order reduction grammars
We present an algorithm which, for given , generates an unambiguous
regular tree grammar defining the set of combinatory logic terms, over the set
of primitive combinators, requiring exactly normal-order
reduction steps to normalize. As a consequence of Curry and Feys's
standardization theorem, our reduction grammars form a complete syntactic
characterization of normalizing combinatory logic terms. Using them, we provide
a recursive method of constructing ordinary generating functions counting the
number of -combinators reducing in normal-order reduction steps.
Finally, we investigate the size of generated grammars, giving a primitive
recursive upper bound
Simple algebraic data types for C
ADT is a simple tool in the spirit of Lex and Yacc that makes algebraic data types and a restricted form of pattern matching on those data types as found in SML available in C programs. ADT adds runtime checks, which make C programs written with the aid of ADT less likely to dereference a NULL pointer. The runtime tests may consume a significant amount of CPU time; hence they can be switched off once the program is suitably debugged
Combinatorial operads from monoids
We introduce a functorial construction which, from a monoid, produces a
set-operad. We obtain new (symmetric or not) operads as suboperads or quotients
of the operads obtained from usual monoids such as the additive and
multiplicative monoids of integers and cyclic monoids. They involve various
familiar combinatorial objects: endofunctions, parking functions, packed words,
permutations, planar rooted trees, trees with a fixed arity, Schr\"oder trees,
Motzkin words, integer compositions, directed animals, and segmented integer
compositions. We also recover some already known (symmetric or not) operads:
the magmatic operad, the associative commutative operad, the diassociative
operad, and the triassociative operad. We provide presentations by generators
and relations of all constructed nonsymmetric operads.Comment: 42 pages. Complete version of the extended abstracts arXiv:1208.0920
and arXiv:1208.092
Operads from posets and Koszul duality
We introduce a functor from the category of posets to the category
of nonsymmetric binary and quadratic operads, establishing a new connection
between these two categories. Each operad obtained by the construction provides a generalization of the associative operad because all of its
generating operations are associative. This construction has a very singular
property: the operads obtained from are almost never basic. Besides,
the properties of the obtained operads, such as Koszulity, basicity,
associative elements, realization, and dimensions, depend on combinatorial
properties of the starting posets. Among others, we show that the property of
being a forest for the Hasse diagram of the starting poset implies that the
obtained operad is Koszul. Moreover, we show that the construction
restricted to a certain family of posets with Hasse diagrams satisfying some
combinatorial properties is closed under Koszul duality.Comment: 40 page
Computing FO-Rewritings in EL in Practice: from Atomic to Conjunctive Queries
A prominent approach to implementing ontology-mediated queries (OMQs) is to
rewrite into a first-order query, which is then executed using a conventional
SQL database system. We consider the case where the ontology is formulated in
the description logic EL and the actual query is a conjunctive query and show
that rewritings of such OMQs can be efficiently computed in practice, in a
sound and complete way. Our approach combines a reduction with a decomposed
backwards chaining algorithm for OMQs that are based on the simpler atomic
queries, also illuminating the relationship between first-order rewritings of
OMQs based on conjunctive and on atomic queries. Experiments with real-world
ontologies show promising results
Generating rewritable abstract syntax trees - A foundation for the rapid development of source code transformation tools
Abstract. Building a production-quality refactoring engine or similar source code transformation tool traditionally requires a large amount of hand-written, language-specific support code. We describe a system which reduces this overhead by allowing both a parser and a fully rewritable AST to be generated automatically from an annotated grammar, requiring little or no additional handwritten code. The rewritable AST is ideal for implementing program transformations that preserve the formatting of the original sources, including spacing and comments, and the system can be augmented to allow transformation of Cpreprocessed sources even when the target language is not C or C++. Moreover, the AST design is fully customizable, allowing it to resemble a hand-coded tree. The amount of required annotation is typically quite small, and the annotated grammar is often an order of magnitude smaller than the generated code
An introduction to description logics and query rewriting
This chapter gives an overview of the description logics underlying the OWL 2 Web Ontology Language and its three tractable profiles, OWL 2 RL, OWL 2 EL and OWL 2 QL. We consider the syntax and semantics of these description logics as well as main reasoning tasks and their computational complexity. We also discuss the semantical foundations for fist-order and datalog rewritings of conjunctive queries over knowledge bases given in the OWL2 profiles, and outline the architecture of the ontology-based data access system Ontop
Reasoning in Many Dimensions : Uncertainty and Products of Modal Logics
Probabilistic Description Logics (ProbDLs) are an extension of Description Logics that are designed to capture uncertainty. We study problems related to these logics. First, we investigate the monodic fragment of Probabilistic first-order logic, show that it has many nice properties, and are able to explain the complexity results obtained for ProbDLs. Second, in order to identify well-behaved, in best-case tractable ProbDLs, we study the complexity landscape for different fragments of ProbEL; amongst others, we are able to identify a tractable fragment. We then study the reasoning problem of ontological query answering, but apply it to probabilistic data. Therefore, we define the framework of ontology-based access to probabilistic data and study the computational complexity therein. In the final part of the thesis, we study the complexity of the satisfiability problem in the two-dimensional modal logic KxK. We are able to close a gap that has been open for more than ten years
BSML: A Binding Schema Markup Language for Data Interchange in Problem Solving Environments (PSEs)
We describe a binding schema markup language (BSML) for describing data
interchange between scientific codes. Such a facility is an important
constituent of scientific problem solving environments (PSEs). BSML is designed
to integrate with a PSE or application composition system that views model
specification and execution as a problem of managing semistructured data. The
data interchange problem is addressed by three techniques for processing
semistructured data: validation, binding, and conversion. We present BSML and
describe its application to a PSE for wireless communications system design
28th International Symposium on Temporal Representation and Reasoning (TIME 2021)
The 28th International Symposium on Temporal Representation and Reasoning (TIME 2021) was planned to take place in Klagenfurt, Austria, but had to move to an online conference due to the insecurities and restrictions caused by the pandemic. Since its frst edition in 1994, TIME Symposium is quite unique in the panorama of the scientifc conferences as its main goal is to bring together researchers from distinct research areas involving the management and representation of temporal data as well as the reasoning about temporal aspects of information. Moreover, TIME Symposium aims to bridge theoretical and applied research, as well as to serve as an interdisciplinary forum for exchange among researchers from the areas of artifcial intelligence, database management, logic and verifcation, and beyond
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