69,027 research outputs found
An Improved Implementation and Abstract Interface for Hybrid
Hybrid is a formal theory implemented in Isabelle/HOL that provides an
interface for representing and reasoning about object languages using
higher-order abstract syntax (HOAS). This interface is built around an HOAS
variable-binding operator that is constructed definitionally from a de Bruijn
index representation. In this paper we make a variety of improvements to
Hybrid, culminating in an abstract interface that on one hand makes Hybrid a
more mathematically satisfactory theory, and on the other hand has important
practical benefits. We start with a modification of Hybrid's type of terms that
better hides its implementation in terms of de Bruijn indices, by excluding at
the type level terms with dangling indices. We present an improved set of
definitions, and a series of new lemmas that provide a complete
characterization of Hybrid's primitives in terms of properties stated at the
HOAS level. Benefits of this new package include a new proof of adequacy and
improvements to reasoning about object logics. Such proofs are carried out at
the higher level with no involvement of the lower level de Bruijn syntax.Comment: In Proceedings LFMTP 2011, arXiv:1110.668
PyZX: Large Scale Automated Diagrammatic Reasoning
The ZX-calculus is a graphical language for reasoning about ZX-diagrams, a
type of tensor networks that can represent arbitrary linear maps between
qubits. Using the ZX-calculus, we can intuitively reason about quantum theory,
and optimise and validate quantum circuits. In this paper we introduce PyZX, an
open source library for automated reasoning with large ZX-diagrams. We give a
brief introduction to the ZX-calculus, then show how PyZX implements methods
for circuit optimisation, equality validation, and visualisation and how it can
be used in tandem with other software. We end with a set of challenges that
when solved would enhance the utility of automated diagrammatic reasoning.Comment: In Proceedings QPL 2019, arXiv:2004.1475
SWI-Prolog and the Web
Where Prolog is commonly seen as a component in a Web application that is
either embedded or communicates using a proprietary protocol, we propose an
architecture where Prolog communicates to other components in a Web application
using the standard HTTP protocol. By avoiding embedding in external Web servers
development and deployment become much easier. To support this architecture, in
addition to the transfer protocol, we must also support parsing, representing
and generating the key Web document types such as HTML, XML and RDF.
This paper motivates the design decisions in the libraries and extensions to
Prolog for handling Web documents and protocols. The design has been guided by
the requirement to handle large documents efficiently. The described libraries
support a wide range of Web applications ranging from HTML and XML documents to
Semantic Web RDF processing.
To appear in Theory and Practice of Logic Programming (TPLP)Comment: 31 pages, 24 figures and 2 tables. To appear in Theory and Practice
of Logic Programming (TPLP
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Transformation of propositional calculus statements into integer and mixed integer programs: An approach towards automatic reformulation
A systematic procedure for transforming a set of logical statements or logical conditions imposed on a model into an Integer Linear Progamming (ILP) formulation Mixed Integer Programming (MIP) formulation is presented. An ILP stated as a system of linear constraints involving integer variables and an objective function, provides a powerful representation of decision problems through a tightly interrelated closed system of choices. It supports direct representation of logical (Boolean or prepositional calculus) expressions. Binary variables (hereafter called logical variables) are first introduced and methods of logically connecting these to other variables are then presented. Simple constraints can be combined to construct logical relationships and the methods of formulating these are discussed. A reformulation procedure which uses the extended reverse polish representation of a compound logical form is then described. These reformulation procedures are illustrated by two examples. A scheme of implementation.ithin an LP modelling system is outlined
Predicting Network Attacks Using Ontology-Driven Inference
Graph knowledge models and ontologies are very powerful modeling and re
asoning tools. We propose an effective approach to model network attacks and
attack prediction which plays important roles in security management. The goals
of this study are: First we model network attacks, their prerequisites and
consequences using knowledge representation methods in order to provide
description logic reasoning and inference over attack domain concepts. And
secondly, we propose an ontology-based system which predicts potential attacks
using inference and observing information which provided by sensory inputs. We
generate our ontology and evaluate corresponding methods using CAPEC, CWE, and
CVE hierarchical datasets. Results from experiments show significant capability
improvements comparing to traditional hierarchical and relational models.
Proposed method also reduces false alarms and improves intrusion detection
effectiveness.Comment: 9 page
Encoding Classifications as Lightweight Ontologies
Classifications have been used for centuries with the goal of cataloguing and searching large sets of objects. In the early days it was mainly books; lately it has also become Web pages, pictures and any kind of electronic information items. Classifications describe their contents using natural language labels, which has proved very effective in manual classification. However natural language labels show their limitations when one tries to automate the process, as they make it very hard to reason about classifications and their contents. In this paper we introduce the novel notion of Formal Classification, as a graph structure where labels are written in a propositional concept language. Formal Classifications turn out to be some form of lightweight ontologies. This, in turn, allows us to reason about them, to associate to each node a normal form formula which univocally describes its contents, and to reduce document classification to reasoning about subsumption
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