David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jonathan Jenkins Ichikawa
Jack Alan Reynolds
Learn more about PhilPapers
Axiomathes 23 (1):137- 164 (2013)
In this paper it is shown that Heyting and Co-Heyting mereological systems provide a convenient conceptual framework for spatial reasoning, in which spatial concepts such as connectedness, interior parts, (exterior) contact, and boundary can be defined in a natural and intuitively appealing way. This fact refutes the wide-spread contention that mereology cannot deal with the more advanced aspects of spatial reasoning and therefore has to be enhanced by further non-mereological concepts to overcome its congenital limitations. The allegedly unmereological concept of boundary is treated in detail and shown to be essentially affected by mereological considerations. More precisely, the concept of boundary turns out to be realizable in a variety of different mereologically grounded versions. In particular, every part K of a Heyting algebra H gives rise to a well-behaved K-relative boundary operator.
|Keywords||Mereology Heyting algebras Co-Heyting algebras Topology (Non-)Tangential Parts Contact Relation Boundary Representation|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
Roberto Casati & Achille C. Varzi (1999). Parts and Places. The Structures of Spatial Representation. The MIT Press.
Paul Hovda (2009). What Is Classical Mereology? Journal of Philosophical Logic 38 (1):55 - 82.
Achille C. Varzi (1996). Parts, Wholes, and Part-Whole Relations: The Prospects of Mereotopology. Data and Knowledge Engineering 20:259–286.
Alfred Tarski (1941). On the Calculus of Relations. Journal of Symbolic Logic 6 (3):73-89.
Barry Smith (1996). Mereotopology: A Theory of Parts and Boundaries. Data and Knowledge Engineering 20:287–303.
Citations of this work BETA
No citations found.
Similar books and articles
M. Abad, J. P. Díaz Varela, L. A. Rueda & A. M. Suardíaz (2000). Varieties of Three-Valued Heyting Algebras with a Quantifier. Studia Logica 65 (2):181-198.
Valeria Castaño & Marcela Muñoz Santis (2011). Subalgebras of Heyting and De Morgan Heyting Algebras. Studia Logica 98 (1-2):123-139.
Sergio A. Celani & Hernán J. San Martín (2012). Frontal Operators in Weak Heyting Algebras. Studia Logica 100 (1-2):91-114.
Guram Bezhanishvili (1999). Varieties of Monadic Heyting Algebras Part II: Duality Theory. Studia Logica 62 (1):21-48.
B. A. Davey & H. A. Priestley (1996). Optimal Natural Dualities for Varieties of Heyting Algebras. Studia Logica 56 (1-2):67 - 96.
Leo Esakia & Benedikt Löwe (2012). Fatal Heyting Algebras and Forcing Persistent Sentences. Studia Logica 100 (1-2):163-173.
Guram Bezhanishvili (1998). Varieties of Monadic Heyting Algebras. Part I. Studia Logica 61 (3):367-402.
H. P. Sankappanavar (2011). Expansions of Semi-Heyting Algebras I: Discriminator Varieties. Studia Logica 98 (1-2):27-81.
Piero Pagliani, Intrinsic Co-Heyting Boundaries and Information Incompleteness in Rough Set Analysis.
Brian A. Davey & John C. Galati (2003). A Coalgebraic View of Heyting Duality. Studia Logica 75 (3):259 - 270.
Luisa Iturrioz (1995). Symmetrical Heyting Algebras with a Finite Order Type of Operators. Studia Logica 55 (1):89 - 98.
Andrzej Sendlewski (1990). Nelson Algebras Through Heyting Ones: I. Studia Logica 49 (1):105-126.
Fabio Bellissima (1986). Finitely Generated Free Heyting Algebras. Journal of Symbolic Logic 51 (1):152-165.
Guram Bezhanishvili (2000). Varieties of Monadic Heyting Algebras. Part III. Studia Logica 64 (2):215-256.
Added to index2011-09-18
Total downloads552 ( #1,984 of 2,149,850 )
Recent downloads (6 months)61 ( #6,601 of 2,149,850 )
How can I increase my downloads?