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A first-order logic for string diagrams [article]

Aleks Kissinger, David Quick
2015 arXiv   pre-print
-boxes to a fully-fledged first order logic called with conjunction, implication, and universal quantification over !-boxes. This logic, called !  ...  While this does greatly increase the proving power of string diagrams, previous attempts to go beyond equational reasoning have been largely ad hoc, owing to the lack of a suitable logical framework for  ...  -tensors As mentioned in the intro, a string diagram with !-boxes represents a family of string diagrams, where the sub-diagram in the !-box has been copied an arbitrary number of times.  ... 
arXiv:1505.00343v1 fatcat:kn5f6ycnwfhofmjpmjftcaymvu

Logic and the Generative Power of Autosegmental Phonology

Adam Jardine
2014 Proceedings of the Annual Meetings on Phonology  
diagrams with monadic second-order logic is introduced.  ...  Monadic second order logic provides a mathematically rigorous way of studying autosegmental formalisms, and its complexity is well understood.  ...  A methodology for a model-theoretic study of autosegmental phonology with monadic second-order logic is introduced.  ... 
doi:10.3765/amp.v1i1.4 fatcat:ja63krgrivhv5dmeywnuayqt3q

Proof Orders for Decreasing Diagrams

Bertram Felgenhauer, Vincent Van Oostrom, Marc Herbstritt
2013 International Conference on Rewriting Techniques and Applications  
We present and compare some well-founded proof orders for decreasing diagrams.  ...  We extend these results to obtain a decreasing diagrams technique for confluence modulo.  ...  Acknowledgements The first author is supported by FWF (Austrian Science Fund) project P22467. The question of completeness (Section 5.2) was raised by Jouannaud.  ... 
doi:10.4230/lipics.rta.2013.174 dblp:conf/rta/FelgenhauerO13 fatcat:y5dqm24cvzcfxfkzg7swi5ipde

Strings from Logic [article]

Christof Schmidhuber
2000 arXiv   pre-print
What are strings made of? The possibility is discussed that strings are purely mathematical objects, made of logical axioms.  ...  More precisely, proofs in simple logical calculi are represented by graphs that can be interpreted as the Feynman diagrams of certain large-N field theories. Each vertex represents an axiom.  ...  Schmidhuber for encouragement, A. Beliakova, M. Hutter and B. Scarpellini for comments on the manuscript, and the audience at CERN for a lively seminar.  ... 
arXiv:hep-th/0011065v1 fatcat:2ijbb2igqbfslnnrln5ilug5ba

Fast Automated Reasoning over String Diagrams using Multiway Causal Structure [article]

Jonathan Gorard, Manojna Namuduri, Xerxes D. Arsiwalla
2021 arXiv   pre-print
We introduce an intuitive algorithmic methodology for enacting automated rewriting of string diagrams within a general double-pushout (DPO) framework, in which the sequence of rewrites is chosen in accordance  ...  semantics for the full multiway evolution causal graph of a generic Wolfram model hypergraph rewriting system.  ...  Spivak and Stephen Wolfram for useful conversations and/or suggestions.  ... 
arXiv:2105.04057v1 fatcat:zjfepnkfubbu5pk3fmng6tibge

A Method of Understanding Conceptual Diagrams

Noriyoshi Yoneda, Koichi Kise, Shinobu Takamatsu, Kunio Fukunaga
1994 IAPR International Workshop on Machine Vision Applications  
In conceptual diagrams, however, a single geometric entity plays various semantic roles for representing concepts, becanse there are no strict rules for writing conceptual diagmms.  ...  A conceptual diagram is a line drawing which represents semantic structure of concepts usirtg simple yeometric entities. This paper presents a method of understanding conceptual diagrams.  ...  For exaniple, a line in Fig. 1 Conceptual Diagrams Let us start with considering the physical and logical structure of conceptual diagrams.  ... 
dblp:conf/mva/YonedaKTF94 fatcat:mbrees2uw5dn7k24mhpfnkhjfm

Strengthening SAT-Based Validation of UML/OCL Models by Representing Collections as Relations [chapter]

Mirco Kuhlmann, Martin Gogolla
2012 Lecture Notes in Computer Science  
Essential OCL operations like role navigation, object selection by stating properties and the first order logic universal and existential quantifiers base upon or result in collections.  ...  ., sets, bags, ordered sets and sequences, play a central role in UML and OCL models.  ...  /HOL a proof assistant for higher-order logic (Nitpick) [2]  ... 
doi:10.1007/978-3-642-31491-9_5 fatcat:ndr7cc42ljeglikrtnssdy6j64

Functorial Boxes in String Diagrams [chapter]

Paul-André Melliès
2006 Lecture Notes in Computer Science  
String diagrams were introduced by Roger Penrose as a handy notation to manipulate morphisms in a monoidal category.  ...  This is not the case however, at least because string diagrams do not accomodate boxes -a key ingredient in these pictorial systems.  ...  I thank them for their precious insights and advice. I am also grateful to Nicolas Tabareau for motivating this work by his ongoing study of trace operators  ... 
doi:10.1007/11874683_1 fatcat:zphjcspjybch7ax6wqx7jox6vy

Proof Diagrams for Multiplicative Linear Logic

Matteo Acclavio
2017 Electronic Proceedings in Theoretical Computer Science  
In this paper we give an interpretation of proof nets in the syntax of string diagrams.  ...  Additional machinery as switching, jumps and graph connectivity is needed in order to ensure correspondence between a proof structure and a correct proof in sequent calculus.  ...  of string diagrams suitable for interpreting linear logic proof derivations.  ... 
doi:10.4204/eptcs.238.2 fatcat:o237qwrf55chhmjztvajgfdws4

Some Remarks on the Geometry of Grammar [article]

Marc Dymetman
1999 arXiv   pre-print
Then we move in Section 2 to a presentation of cancellation diagrams and show how they can be used computationally.  ...  This paper, following (Dymetman:1998), presents an approach to grammar description and processing based on the geometry of cancellation diagrams, a concept which plays a central role in combinatorial group  ...  Figure 9 : 9 A diagram establishing the relationship between a logical form and a phonological string.  ... 
arXiv:cs/9903007v1 fatcat:ohahgnsvcrbrpnae7dd73kvb6a

Dialog interface for dynamic data models [article]

Vojtech Prehnal
2011 arXiv   pre-print
It will also cut the price and shorten the development time of the information systems dramatically, because common business logic will not have to be implemented for each individual table and the major  ...  string FilterExpression) where Skip and Take are paging parameters (the index of the first item and the number of items to retrieve), OrderExpression is the content of SQL order by clause and FilterExpression  ...  ReadTotal(string TableName, string FilterExpression) Client Server int Communication diagram: Class diagram: table retrieval : retrieval ReadItems(string TableName, int Skip, int Take, string  ... 
arXiv:1101.5938v1 fatcat:imhyoncubffrdhcrn5qc2bpvnm

Recognition of Handwritten Numerals Using a Decision Graph

Sumio Katsuragi, Hiroshi Genchi, Ken-ichi Mori, Sadakazu Watanabe
1969 International Joint Conference on Artificial Intelligence  
The decision graph consists of a set of decision transition diagrams to be compared with the string of extracted features and a penalty count system to detect the optimum match.  ...  High flexibility against unlimited variability of handwritten character shapes is achieved by means of a stored logic system using rewritable magnetic core memory.  ...  Sawasaki, Director of the Central Research Laboratory for their constant encouragement.  ... 
dblp:conf/ijcai/KatsuragiGMW69 fatcat:5l6u5zd66vcfzl57kzs6qehkpi

Proof Diagrams for Multiplicative Linear Logic: Syntax and Semantics

Matteo Acclavio
2018 Journal of automated reasoning  
Furthermore, we can use this syntax to define a denotational semantics for multiplicative linear logic with units by means of equivalence classes of proof diagrams modulo a terminating rewriting.  ...  The syntax of string diagrams authorizes the definition of a framework where the sequentializability of a term, i.e. deciding whether the term corresponds to a correct derivation, can be verified in linear  ...  A special acknowledgment to Yves Guiraud who wrote (and upgraded for the scope) the latex package for string diagrams representations [13] employed in the present manuscript.  ... 
doi:10.1007/s10817-018-9466-4 fatcat:trdzt7r7bjgenf23mmd5exmbpu

On the Composition of Design Patterns

Ian Bayley, Hong Zhu
2008 2008 The Eighth International Conference on Quality Software  
a pattern with a subset of components as the key.  ...  Design patterns are usually applied in a composed form with each other.  ...  In our previous work, we developed a technique for the formal specification of design patterns in first order logic.  ... 
doi:10.1109/qsic.2008.32 dblp:conf/qsic/BayleyZ08 fatcat:7b6u6atkufei7mxig6gg2jofvu

Foundations of brick diagrams [article]

Jules Hedges, Jelle Herold
2019 arXiv   pre-print
In particular, we discuss the close relationship between string diagrams, pasting diagrams, linear logic proof trees and k-d trees, the last being a data structure from computational geometry and computer  ...  We discuss the foundations of 2-dimensional graphical languages, with a view towards their computer implementation in a 'compiler' for monoidal categories.  ...  The first is categories of string diagrams modulo isotopy, and the second is as categories of linear logic proof trees modulo rewrites.  ... 
arXiv:1908.10660v1 fatcat:d7yrk5ms4neqplnmguqxq5kgyu
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