Meta-Interpretive Learners, like most ILP systems, learn by searching for a correct hypothesis in the space, powerset of all constructible clauses. We show how this exponentially-growing search can be replaced construction Top program: set clauses hypotheses that is itself hypothesis. give an algorithm program and it constructs polynomial time from finite number examples. implement our Prolog a...

in this work, we describe an adjunction between the comma category of set-based monads under the v -powerset monad and the category of associative lax extensions of set-based monads to the category of v -relations. in the process, we give a general construction of the kleisli extension of a monad to the category of v-relations.

When analyzing a large amount of data, analysts often define groups over data elements that share certain properties. Using these groups as the unit of analysis not only reduces the data volume, but also allows detecting various patterns in the data. This involves analyzing intersection relations between these groups, and how the element attributes vary between these intersections. This kind of...

Automata over infinite words provide a powerful framework, which we can use to solve various decision problems. However, the automatized reasoning with restricted classes of automata over infinite words is often simpler and more efficient. For instance, weak deterministic Büchi automata, which recognize the ω-regular languages in the Borel class Fσ ∩Gδ, can be handled algorithmically almost as ...

In this paper a binary relation between L-sets, called attachment, is defined by means of a suitable family of completely coprime filters in L. Examples are given using several kinds of lattice-ordered algebras and a class of attachments is determined whose elements generalize Pu-Liu’s quasi-coincidence relation. Mapping any L-set on X to the set of the attached L-points one gets a frame map fr...

We present here a view on abstraction based on the relation between sentences in a partially ordered language L and truth values of these sentences on a set of instances W . In Formal Concept Analysis, this relation is materialized as a lattice denoted as G that relates L and the powerset P(W )). We show here that projections on a lattice (here either L or the powerset P(W )) that are known to ...

The powerset operator, P, is an operator which (1) sends sets to sets,(2) is defined by a positive formula and (3) raises the cardinality of its argument, i.e., |P(x)| > |x|. As a consequence of (3), P has a proper class as least fixed point (the universe itself). In this paper we address the questions: (a) How does P contribute to the generation of the class of all positive operators? (b) Are ...

Besides all the attention given to lattice constructions, it is common to find some very interesting nonlattice constellations, as Construction C, for example, which also has relevant applications in communication problems (multi-level coding, multi-stage decoding, good quantization efficieny). In this work we present a constellation which is a subset of Construction C, based on inter-level cod...

Grail is a package for symbolic manipulation of nite-state automata and regular expressions. It provides most standard operations on automata and expressions, including minimization, subset construction, conversion between automata and regular expressions , and language enumeration and testing. Grail's objects are parameterizable; users can provide their own classes to deene the input alphabet ...