Results 1  10
of
16
Full completeness of the multiplicative linear logic of chu spaces
 Proc. IEEE Logic in Computer Science 14
, 1999
"... We prove full completeness of multiplicative linear logic (MLL) without MIX under the Chu interpretation. In particular we show that the cutfree proofs of MLL theorems are in a natural bijection with the binary logical transformations of the corresponding operations on the category of Chu spaces on ..."
Abstract

Cited by 27 (8 self)
 Add to MetaCart
We prove full completeness of multiplicative linear logic (MLL) without MIX under the Chu interpretation. In particular we show that the cutfree proofs of MLL theorems are in a natural bijection with the binary logical transformations of the corresponding operations on the category of Chu spaces on a twoletter alphabet. This is the online version of the paper of the same title appearing in the LICS’99 proceedings. 1
Rate distortion manifolds as model spaces for cognitive information
 In preparation
, 2007
"... The rate distortion manifold is considered as a carrier for elements of the theory of information proposed by C. E. Shannon combined with the semantic precepts of F. Dretske’s theory of communication. This type of information space was suggested by R. Wallace as a possible geometric–topological desc ..."
Abstract

Cited by 15 (9 self)
 Add to MetaCart
(Show Context)
The rate distortion manifold is considered as a carrier for elements of the theory of information proposed by C. E. Shannon combined with the semantic precepts of F. Dretske’s theory of communication. This type of information space was suggested by R. Wallace as a possible geometric–topological descriptive model for incorporating a dynamic information based treatment of the Global Workspace theory of B. Baars. We outline a more formal mathematical description for this class of information space and further clarify its structural content and overall interpretation within prospectively a broad range of cognitive situations that apply to individuals, human institutions, distributed cognition and massively parallel intelligent machine design. Povzetek: Predstavljena je formalna definicija prostora za opisovanje kognitivnih procesov. 1
Chu’s Construction: A Prooftheoretic Approach
 LOGIC FOR CONCURRENCY AND SYNCHRONISATION”, KLUWER TRENDS IN LOGIC N.18, 2003, PP.93114. LAMBDA CALCULUS 37
, 2001
"... ..."
EventState Duality: The Enriched Case
"... Enriched categories have been applied in the past to both eventoriented true concurrency models and stateoriented information systems, with no evident relationship between the two. Ordinary Chu spaces expose a natural duality between partially ordered temporal spaces (pomsets, event structures), a ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
(Show Context)
Enriched categories have been applied in the past to both eventoriented true concurrency models and stateoriented information systems, with no evident relationship between the two. Ordinary Chu spaces expose a natural duality between partially ordered temporal spaces (pomsets, event structures), and partially ordered information systems.
A categorical semantics for polarized mall
 Ann. Pure Appl. Logic
"... In this paper, we present a categorical model for Multiplicative Additive Polarized Linear Logic MALLP, which is the linear fragment (without structural rules) of Olivier Laurent’s Polarized Linear Logic. Our model is based on an adjunction between reflective/coreflective full subcategories C−/C+ of ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
(Show Context)
In this paper, we present a categorical model for Multiplicative Additive Polarized Linear Logic MALLP, which is the linear fragment (without structural rules) of Olivier Laurent’s Polarized Linear Logic. Our model is based on an adjunction between reflective/coreflective full subcategories C−/C+ of an ambient ∗autonomous category C (with products). Similar structures were first introduced by M. Barr in the late 1970’s in abstract duality theory and more recently in work on game semantics for linear logic. The paper has two goals: to discuss concrete models and to present various completeness theorems. As concrete examples, we present (i) a hypercoherence model, using Ehrhard’s hereditary/antihereditary objects, (ii) a Chuspace model, (iii) a double gluing model over our categorical framework, and (iv) a model based on iterated double gluing over a ∗autonomous category. For the multiplicative fragment MLLP of MALLP, we present both weakly full (Läuchlistyle) as well as full completeness theorems, using a polarized version of functorial
Morphisms in context
 Conceptual Structures: Common Semantics for Sharing Knowledge, Proceedings of ICCS 2005, Springer LNAI 3596 (2005
"... Abstract. Morphisms constitute a general tool for modelling complex relationships between mathematical objects in a disciplined fashion. In Formal Concept Analysis (FCA), morphisms can be used for the study of structural properties of knowledge represented in formal contexts, with applications to da ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
(Show Context)
Abstract. Morphisms constitute a general tool for modelling complex relationships between mathematical objects in a disciplined fashion. In Formal Concept Analysis (FCA), morphisms can be used for the study of structural properties of knowledge represented in formal contexts, with applications to data transformation and merging. In this paper we present a comprehensive treatment of some of the most important morphisms in FCA and their relationships, including dual bonds, scale measures, infomorphisms, and their respective relations to Galois connections. We summarize our results in a concept lattice that cumulates the relationships among the considered morphisms. The purpose of this work is to lay a foundation for applications of FCA in ontology research and similar areas, where morphisms help formalize the interplay among distributed knowledge bases. 1
A Parigotstyle linear λcalculus for Full intuitionistic Linear Logic
, 2005
"... This paper describes a natural deduction formulation for Full Intuitionistic Linear Logic (FILL), an intriguing variation of multiplicative linear logic, due to Hyland and de Paiva. The system FILL resembles intuitionistic logic, in that all its connectives are independent, but resembles classical l ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
(Show Context)
This paper describes a natural deduction formulation for Full Intuitionistic Linear Logic (FILL), an intriguing variation of multiplicative linear logic, due to Hyland and de Paiva. The system FILL resembles intuitionistic logic, in that all its connectives are independent, but resembles classical logic in that its sequentcalculus formulation has intrinsic multiple conclusions. From the intrinsic multiple conclusions comes the inspiration to modify Parigot’s natural deduction systems for classical logic, to produce a natural deduction formulation and a term assignment system for FILL. keywords: linear logic, λµcalculus, CurryHoward isomorphism 1
Bifinite Chu spaces
"... ABSTRACT. This paper studies colimits of sequences of finite Chu spaces and their ramifications. We consider three base categories of Chu spaces: the generic Chu spaces (C), the extensional Chu spaces (E), and the biextensional Chu spaces (B). The main results are: (1) a characterization of monics i ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
(Show Context)
ABSTRACT. This paper studies colimits of sequences of finite Chu spaces and their ramifications. We consider three base categories of Chu spaces: the generic Chu spaces (C), the extensional Chu spaces (E), and the biextensional Chu spaces (B). The main results are: (1) a characterization of monics in each of the three categories; (2) existence (or the lack thereof) of colimits and a characterization of finite objects in each of the corresponding categories using monomorphisms/injections (denoted as iC, iE, and iB, respectively); (3) a formulation of bifinite Chu spaces with respect to iC; (4) the existence
Chu Spaces: Towards New Foundations for Fuzzy Logic and Fuzzy Control, with Applications to Information Flow on the World Wide Web
 Proceedings of the 18th International Conference of the North American Fuzzy Information Society NAFIPS'99
, 1999
"... We show that Chu spaces, a new formalism used to describe parallelism and information flow, provide uniform explanations for different choices of fuzzy methodology, such as choices of fuzzy logical operations, of membership functions, of defuzzification, etc. 1. What are Chu spaces? 1.1. World accor ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
(Show Context)
We show that Chu spaces, a new formalism used to describe parallelism and information flow, provide uniform explanations for different choices of fuzzy methodology, such as choices of fuzzy logical operations, of membership functions, of defuzzification, etc. 1. What are Chu spaces? 1.1. World according to classical physics It is well known that measurements can change the measured object: e.g., most methods of chemical analysis destroy a part of the analyzed substance; testing a car often means damaging it, etc. However, in classical (prequantum) physics it was assumed that in principle, we can make this adverse influence as small as possible. Therefore, ideally, each measurement can be described as a function r(x) from the set of all objects X to the set K of all measurement results. These measurements lead to a complete knowledge in the sense that an object x can be uniquely reconstructed from the results r(x) of all such measurements. 1.2. Nondeterminism in modern physics: enter Chu spaces In modern physics, starting from quantum mechanics, it was realized that ideal noninfluencing measurements are impossible: the more accurately we measure, the more we change the object of measurement. As a result, it is not possible to uniquely reconstruct an object from measurement results. In other words, each measurement is a function r(x, y) of two variables: an object x and a (not completely known) measuring device y. Such a function describes a socalled Chu space
Modeling noniterated system behavior with Chu spaces
, 2008
"... Abstract: We present an algorithm for generating Chu space models of the behaviors of arbitrarily complex noniterated systems including those with Ntype dependencies. The generated Chu space can be used for verification of system properties. The application of the model generation algorithm is il ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
Abstract: We present an algorithm for generating Chu space models of the behaviors of arbitrarily complex noniterated systems including those with Ntype dependencies. The generated Chu space can be used for verification of system properties. The application of the model generation algorithm is illustrated with a few examples. KeyWords: concurrency, Chu spaces, system behavior modeling, Ntype dependencies 1