An Axiom System for a Spatial Logic with Convexity
Author's Profile
Adam Trybus, PhD
brianervinmamaril@gmail.com
The University of Manchester
Trybus' Works
An Axiom System for a Spatial Logic with Convexity
A spatial logic is any formal language with geometric interpretation. Research on region-based spatial logics, where variables are set to range over certain subsets of geometric space, have been investigated recently within the qualitative spatial reasoning paradigm in AI. We axiomatised the theory... Read More
ETD Test 20
ETD Test 20
Abstract: A spatial logic is any formal language with geometric interpretation. Research on region-based spatial logics, where variables are set to range over certain subsets of geometric space, have been investigated recently within the qualitative spatial reasoning paradigm in AI. We axiomatised the theory of (ROQ(R^2), conv, ≤) , where ROQ(R^2) is the set of regular open rational polygons of the real plane; conv is the convexity property and ≤ is the inclusion relation. We proved soundness and completeness theorems. We also proved several expressiveness results. Additionally, we provide a historical and philosophical overview of the topic and present contemporary results relating to affine spatial logics.
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Author's Profile
Paolini Gianluca PhD
brianervinmamaril@gmail.com
The University of Manchester
Gianluca's Works
Independence in Model Theory and Team Semantics
The subject of this doctoral thesis is the mathematical theory of independence, and its various manifestations in logic and mathematics. The topics covered in this doctoral thesis range from model theory and combinatorial geometry, to database theory, quantum logic and probability logic. This study... Read More
ETD Test Upload 12345
ETD Test Upload 12345
The subject of this doctoral thesis is the mathematical theory of independence, and its various manifestations in logic and mathematics. The topics covered in this doctoral thesis range from model theory and combinatorial geometry, to database theory, quantum logic and probability logic. This study...
Author's Profile
Koushik Pal PhD
brianervinmamaril@gmail.com
The University of Manchester
Pal's Works
Uniform Theory of Multiplicative Valued Difference Fields
The first part of the thesis concerns the existence of model companions of certain unstable theories with automorphisms. Let T be a first-order theory with the strict order property. According to Kikyo and Shelah's theorem, the theory of models of T with a generic automorphism does not have a model... Read More
The first part of the thesis concerns the existence of model companions of certain unstable theories with automorphisms. Let T be a first-order theory with the strict order property. According to Kikyo and Shelah's theorem, the theory of models of T with a generic automorphism does not have a model...