156,385 research outputs found
NiMo syntax: part 1
Many formalisms for the specification for concurrent and distributed systems have emerged. In particular considering boxes and strings approaches. Examples are action calculi, rewriting logic and graph rewriting, bigraphs. The boxes and string metaphor is addressed with different levels of granularity. One of the approaches is to consider a process network as an hypergraph. Based in this general framework, we encode NiMo nets as a class of Annotated hypergraphs. This class is defined by giving the alphabet and the operations used to construct such programs. Therefore we treat only editing operations on labelled hypergraphs and afterwards how this editing operation affects the graph. Graph transformation (execution rules) is not covered here.Postprint (published version
Discourse-Aware Graph Networks for Textual Logical Reasoning
Textual logical reasoning, especially question-answering (QA) tasks with
logical reasoning, requires awareness of particular logical structures. The
passage-level logical relations represent entailment or contradiction between
propositional units (e.g., a concluding sentence). However, such structures are
unexplored as current QA systems focus on entity-based relations. In this work,
we propose logic structural-constraint modeling to solve the logical reasoning
QA and introduce discourse-aware graph networks (DAGNs). The networks first
construct logic graphs leveraging in-line discourse connectives and generic
logic theories, then learn logic representations by end-to-end evolving the
logic relations with an edge-reasoning mechanism and updating the graph
features. This pipeline is applied to a general encoder, whose fundamental
features are joined with the high-level logic features for answer prediction.
Experiments on three textual logical reasoning datasets demonstrate the
reasonability of the logical structures built in DAGNs and the effectiveness of
the learned logic features. Moreover, zero-shot transfer results show the
features' generality to unseen logical texts
Neural-Symbolic Recommendation with Graph-Enhanced Information
The recommendation system is not only a problem of inductive statistics from
data but also a cognitive task that requires reasoning ability. The most
advanced graph neural networks have been widely used in recommendation systems
because they can capture implicit structured information from graph-structured
data. However, like most neural network algorithms, they only learn matching
patterns from a perception perspective. Some researchers use user behavior for
logic reasoning to achieve recommendation prediction from the perspective of
cognitive reasoning, but this kind of reasoning is a local one and ignores
implicit information on a global scale. In this work, we combine the advantages
of graph neural networks and propositional logic operations to construct a
neuro-symbolic recommendation model with both global implicit reasoning ability
and local explicit logic reasoning ability. We first build an item-item graph
based on the principle of adjacent interaction and use graph neural networks to
capture implicit information in global data. Then we transform user behavior
into propositional logic expressions to achieve recommendations from the
perspective of cognitive reasoning. Extensive experiments on five public
datasets show that our proposed model outperforms several state-of-the-art
methods, source code is avaliable at [https://github.com/hanzo2020/GNNLR].Comment: 12 pages, 2 figures, conferenc
Beyond Outerplanarity
We study straight-line drawings of graphs where the vertices are placed in
convex position in the plane, i.e., convex drawings. We consider two families
of graph classes with nice convex drawings: outer -planar graphs, where each
edge is crossed by at most other edges; and, outer -quasi-planar graphs
where no edges can mutually cross. We show that the outer -planar graphs
are -degenerate, and consequently that every
outer -planar graph can be -colored, and this
bound is tight. We further show that every outer -planar graph has a
balanced separator of size . This implies that every outer -planar
graph has treewidth . For fixed , these small balanced separators
allow us to obtain a simple quasi-polynomial time algorithm to test whether a
given graph is outer -planar, i.e., none of these recognition problems are
NP-complete unless ETH fails. For the outer -quasi-planar graphs we prove
that, unlike other beyond-planar graph classes, every edge-maximal -vertex
outer -quasi planar graph has the same number of edges, namely . We also construct planar 3-trees that are not outer
-quasi-planar. Finally, we restrict outer -planar and outer
-quasi-planar drawings to \emph{closed} drawings, where the vertex sequence
on the boundary is a cycle in the graph. For each , we express closed outer
-planarity and \emph{closed outer -quasi-planarity} in extended monadic
second-order logic. Thus, closed outer -planarity is linear-time testable by
Courcelle's Theorem.Comment: Appears in the Proceedings of the 25th International Symposium on
Graph Drawing and Network Visualization (GD 2017
The Sierpinski Object in the Scott Realizability Topos
We study the Sierpinski object in the realizability topos based on
Scott's graph model of the -calculus. Our starting observation is that
the object of realizers in this topos is the exponential , where
is the natural numbers object. We define order-discrete objects by
orthogonality to . We show that the order-discrete objects form a
reflective subcategory of the topos, and that many fundamental objects in
higher-type arithmetic are order-discrete. Building on work by Lietz, we give
some new results regarding the internal logic of the topos. Then we consider
as a dominance; we explicitly construct the lift functor and
characterize -subobjects. Contrary to our expectations the dominance
is not closed under unions. In the last section we build a model for
homotopy theory, where the order-discrete objects are exactly those objects
which only have constant paths
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