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Ollongren A.,Leiden Institute of Advanced Computer Science
Acta Astronautica | Year: 2011

Aristotelian assertive syllogistic logic (without modalities) is embedded in the author's Lingua Cosmica. The well-known basic structures of assertions and conversions between them in this logic are represented in LINCOS. Since these representations correspond with set-theoretic operations, the latter are embedded in LINCOS as well. Based on this valid argumentation in Aristotle's sense is obtained for four important so-called perfect figures. Their constructive (intuitionistic) verifications are of a surprisingly elegant simplicity. © 2010 Elsevier Ltd. Source


Ollongren A.,Leiden Institute of Advanced Computer Science
Acta Astronautica | Year: 2011

In a sequence of papers on the topic of message construction for interstellar communication by means of a cosmic language, the present author has discussed various significant requirements such a lingua should satisfy. The author's Lingua Cosmica is a (meta) system for annotating contents of possibly large-scale messages for ETI. LINCOS, based on formal constructive logic, was primarily designed for dealing with logic contents of messages but is also applicable for denoting structural properties of more general abstractions embedded in such messages. The present paper explains ways and means for achieving this for a special case: recursive entities. As usual two stages are involved: first the domain of discourse is enriched with suitable representations of the entities concerned, after which properties over them can be dealt with within the system itself. As a representative example the case of Russian dolls (Matrjoshka's) is discussed in some detail and relations with linguistic structures in natural languages are briefly exploited. © 2010 Elsevier Ltd. Source


Ollongren A.,Leiden Institute of Advanced Computer Science
Acta Astronautica | Year: 2014

The paper addresses the validation issue for the Lingua Cosmica system: have the results of sequences of reasoning (i.e. conclusions) a universal validity in some sense? LINCOS verifications of a selected set of representative statements are considered. They are compared with proofs of the same statements obtained by means of an existing proof system in computer science. The treatment indicates how formalised descriptive logic reasoning can be transposed from one system to the other. As this kind of reasoning is not bound to a specific system, it possesses an aspect of unversality. © 2013 Published by Elsevier Ltd. on behalf of IAA. Source


Ollongren A.,Leiden Institute of Advanced Computer Science
Acta Astronautica | Year: 2012

In a sequence of papers on the topic of message construction for interstellar communication by means of a cosmic language, representations of various kinds of concepts of reality in a Lingua Cosmica system [1]. Those studied were logic relations of a static character. The present contribution contains an important, fundamental extension: groundwork is done for the purpose of interpreting (dynamic) processes of various sorts in the linguistic system. Individual processes are abstracted in a logic sense and provided with basic properties as termination and communication functions. They can be combined into kinds of processes: sequential and parallel ones represented by only one inductive definition in logic. Based on concepts from the so-called process algebra, processes are provided with channels mapping them to their states. State vectors are introduced to represent states of conglomerates of processes. Communication between processes (locally or globally) is effectuated by means of state transitions. Together with a programmed arbitration function, state vectors play a crucial role in representing communication. With these ingredients possibilities for general interpretations of a wide range of processes in the Lingua Cosmica system come in view. © 2011 Elsevier Ltd. Source


Bonchi F.,University of Lyon | Bonsangue M.,Leiden Institute of Advanced Computer Science | Boreale M.,University of Florence | Rutten J.,Centrum Wiskunde and Informatica | And 4 more authors.
Information and Computation | Year: 2012

Weighted automata are a generalisation of non-deterministic automata where each transition, in addition to an input letter, has also a quantity expressing the weight (e.g. cost or probability) of its execution. As for non-deterministic automata, their behaviours can be expressed in terms of either (weighted) bisimilarity or (weighted) language equivalence. Coalgebras provide a categorical framework for the uniform study of state-based systems and their behaviours. In this work, we show that coalgebras can suitably model weighted automata in two different ways: coalgebras on Set (the category of sets and functions) characterise weighted bisimilarity, while coalgebras on Vect (the category of vector spaces and linear maps) characterise weighted language equivalence. Relying on the second characterisation, we show three different procedures for computing weighted language equivalence. The first one consists in a generalisation of the usual partition refinement algorithm for ordinary automata. The second one is the backward version of the first one. The third procedure relies on a syntactic representation of rational weighted languages. © 2012 Elsevier Inc. All rights reserved. Source

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