Thomas Bittner
Associate Professor
Department of Philosophy and Department of Geography
University at Buffalo, State University of New York
Logical theories are developed, in formal and applied ontology, of the structures that ordinary and scientific descriptions of the world presuppose: parts and wholes, space and time, granularity, and the vagueness that appears wherever those descriptions meet the things they describe.
The theories are developed with particular cases in view: geographic regions whose boundaries no measurement fixes, anatomical structures that a biomedical ontology has to relate to one another, ecological classifications that vary from one scale to the next, and judgments made under vagueness as well as uncertainty. They are stated in first-order or higher-order logic. In current work, indeterminate predicates are also represented in the algebra of stabilizer states, and selected results of the most recent papers are accompanied by machine-checked formalizations.
Research themes
The work has developed along six lines, which share a common question: what has to be true of a domain for a description of it to be correct, and what becomes of correctness when the description is coarser than the domain.
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Mereology and granularity
Axiomatic theories of the part-of, componenthood, and containment relations, and of the granular partitions that determine what counts as one thing at a given level of resolution.
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Vagueness and approximation
Rough location, stratified rough sets, and vague size and distance predicates: formal accounts of judgments that are determinate at one level of granularity and indeterminate at another.
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Space, time, and physical entities
Ontologies of spatial and spatio-temporal regions, of endurants and perdurants, and of what classical mechanics must assume to exist before it can state a law.
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Quantized mereology
The current program: an algebraic semantics for indeterminate predicates built on the stabilizer formalism, in which determinacy, gappy indeterminacy, and correlated indeterminacy are three modes of one representation.
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Geographic information science
The ontological foundations of GIS: the classification and delineation of geographic regions, ecosystem hierarchies, and the semantic interoperability of spatial data.
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Computational realization
Formalizing ontologies in Isabelle/HOL so that the consistency of an axiom set and its consequences are machine-checked, the adequacy of the formalization to the ontology being recorded separately.
The stabilizer program
The program represents a tuple of entities and the predicates jointly applied to it by one algebraic object, a stabilizer state, so that determinacy, gappy indeterminacy, and correlated indeterminacy, together with the questions that reveal or disturb them, are represented within one structure.
The public papers of the series quantify the cost of imposing precision, give a relational theory of mereological judgment, and apply the framework to intelligence analysis. Papers in preparation treat empty regions and identity under indeterminacy, the composition of vague relations across networks of entities, and ecological classification.
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2026
Liquid mereology: vagueness, information capacity, and the cost of precisionUnder review
Submitted to a journal. PhilSci-Archive 30967 -
2026
A relational theory of mereological judgmentUnder review
Submitted to a journal. PhilSci-Archive 30864 -
2026
An algebraic framework for indeterminate predicates: classification, reasoning and dispositional dynamicsUnder review
Submitted to a journal. PhilSci-Archive 30569 -
2025
Quantized mereologyIn press
Journal of Artificial Intelligence Research. PhilSci-Archive 30559 arXiv - 2023
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2019
On the computational realization of formal ontologies: Formalizing an ontology of instantiation in spacetime using Isabelle/HOL as a case study
Applied Ontology 14(3), 251-292. DOI -
2018
Formal ontology of space, time, and physical entities in classical mechanics
Applied Ontology 13(2), 135-179. DOI