Attempts at combining logic and neural networks into neurosymbolic approaches have been on the increase in recent years. In a system, symbolic knowledge assists deep learning, which typically uses sub-symbolic distributed representation, to learn reason higher level of abstraction. We present Logic Tensor Networks (LTN), framework that supports querying, learning reasoning with both rich data a...

Dependency-based Compositional Semantics (DCS) provides a precise and expressive way to model semantics of natural language queries on relational databases, by simple dependency-like trees. Recently abstract denotation is proposed to enable generic logical inference on DCS. In this paper, we discuss some other possibilities to equip DCS with logical inference, and we discuss further on how logi...

New results on fuzzy concepts and concept lattices are presented. The issue of logical precision, a phenomenon that—although completely degenerate in two-valued logic—naturally arises in the context of fuzzy logic is studied. We present basic results regarding logical precision and concept lattices. Since, as far as we know, the phenomenon has not been discussed in literature so far, we briefly...

This is Part 1 of a paper on fibred semantics and combination of logics. It aims to present a methodology for combiningarbitrary logical systems L, , i E I,to form a new system LI . The methodology 'fibres' the semantics 3,of Li into a semantics for L I , and 'weaves' the proof theory (axiomatics) of L, into a proof system of L I . There are various ways of doing this, we distinguish by differe...

We present and analyze inference method called Perception-based Logical Deduction (PbLD) aimed at the treatment of fuzzy IF-THEN rules as linguistically expressed genuine logical implications. Besides the original PbLD, we propose a new balancing variant of PbLD, introduce both variants with fuzzy inputs and study them from the point of view of the interpolativity property.

The MapReduce framework has proved to be very efficient for data-intensive tasks. Earlier work has tried to use MapReduce for large scale reasoning for pD∗ semantics and has shown promising results. In this paper, we move a step forward to consider scalable reasoning on top of semantic data under fuzzy pD∗ semantics (i.e., an extension of OWL pD∗ semantics with fuzzy vagueness). To the best of ...

in this paper, we investigate the l-fuzzy proximities and the relationships betweenl-fuzzy topologies, l-fuzzy topogenous order and l-fuzzy uniformity. first, we show that the category of-fuzzy topological spaces can be embedded in the category of l-fuzzy quasi-proximity spaces as a coreective full subcategory. second, we show that the category of l -fuzzy proximity spaces is isomorphic to the ...