Mereology then and now

This paper offers a critical reconstruction of the motivations that led to the development of mereology as we know it today, along with a brief description of some questions that define current research in the field

Finitely inseparable first-order axiomatized mereotopological theories

This paper will first introduce first-order mereotopological axioms and axiomatized theories which can be found in some recent literature and it will also give a survey of decidability, undecidability as well as other relevant notions. Then the main result to be given in this paper will be the finite inseparability of any mereotopological theory up to atomic general mereotopology (AGEMT) or strong atomic general mereotopology (SAGEMT). Besides, a more comprehensive summary will also be given via making observations about other properties stronger than undecidability

Notes on models of first-order mereological theories

This paper will consider some interesting mereological models and, by looking into them carefully, will clarify some important metalogical issues, such as definability, atomicity and decidability. More precisely, this paper will inquire into what kind of subsets can be defined in certain mereological models, what kind of axioms can guarantee that any member is composed of atoms and what kind of axioms are crucial, by regulating the models in a certain way, for an axiomatized mereological theory to be decidable

Formal Theories of Parthood

A compact overview of the main formal theories of parthood and of their mutual relationships, up to Classical Extensional Mereology. Written as an Appendix to the other essays included in the volume

A Monadic Second-Order Version of Tarski’s Geometry of Solids

In this paper, we are concerned with the development of a general set theory using the single axiom version of Leśniewski’s mereology. The specification of mereology, and further of Tarski’s geometry of solids will rely on the Calculus of Inductive Constructions (CIC). In the first part, we provide a specification of Leśniewski’s mereology as a model for an atomless Boolean algebra using Clay’s ideas. In the second part, we interpret Leśniewski’s mereology in monadic second-order logic using names and develop a full version of mereology referred to as CIC-based Monadic Mereology (λ-MM) allowing an expressive theory while involving only two axioms. In the third part, we propose a modeling of Tarski’s solid geometry relying on λ-MM. It is intended to serve as a basis for spatial reasoning. All parts have been proved using a translation in type theory

Epistemic Modality, Mind, and Mathematics

This book concerns the foundations of epistemic modality. I examine the nature of epistemic modality, when the modal operator is interpreted as concerning both apriority and conceivability, as well as states of knowledge and belief. The book demonstrates how epistemic modality relates to the computational theory of mind; metaphysical modality; the types of mathematical modality; to the epistemic status of large cardinal axioms, undecidable propositions, and abstraction principles in the philosophy of mathematics; to the modal profile of rational intuition; and to the types of intention, when the latter is interpreted as a modal mental state. Chapter \textbf{2} argues for a novel type of expressivism based on the duality between the categories of coalgebras and algebras, and argues that the duality permits of the reconciliation between modal cognitivism and modal expressivism. Chapter \textbf{3} provides an abstraction principle for epistemic intensions. Chapter \textbf{4} advances a topic-sensitive two-dimensional truthmaker semantics, and provides three novel interpretations of the framework along with the epistemic and metasemantic. Chapter \textbf{5} applies the fixed points of the modal $\mu$-calculus in order to account for the iteration of epistemic states, by contrast to availing of modal axiom 4 (i.e. the KK principle). Chapter \textbf{6} advances a solution to the Julius Caesar problem based on Fine's "criterial" identity conditions which incorporate conditions on essentiality and grounding. Chapter \textbf{7} provides a ground-theoretic regimentation of the proposals in the metaphysics of consciousness and examines its bearing on the two-dimensional conceivability argument against physicalism. The topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapter \textbf{4} is availed of in order for epistemic states to be a guide to metaphysical states in the hyperintensional setting. Chapter \textbf{8} examines the modal commitments of abstractionism, in particular necessitism, and epistemic modality and the epistemology of abstraction. Chapter \textbf{9} examines the modal profile of $\Omega$-logic in set theory. Chapter \textbf{10} examines the interaction between epistemic two-dimensional truthmaker semantics, epistemic set theory, and absolute decidability. Chapter \textbf{11} avails of modal coalgebraic automata to interpret the defining properties of indefinite extensibility, and avails of epistemic two-dimensional semantics in order to account for the interaction of the interpretational and objective modalities thereof. The hyperintensional, topic-sensitive epistemic two-dimensional truthmaker semantics developed in chapter \textbf{2} is applied in chapters \textbf{7}, \textbf{8}, \textbf{10}, and \textbf{11}. Chapter \textbf{12} provides a modal logic for rational intuition and provides four models of hyperintensional semantics. Chapter \textbf{13} examines modal responses to the alethic paradoxes. Chapter \textbf{14} examines, finally, the modal semantics for the different types of intention and the relation of the latter to evidential decision theory

The ontology of haecceities

This thesis deals with the Problem of Distinction, i.e. what explains the distinction of two substances, especially when they are qualitatively indiscernible? It argues that the best solution to this problem is an ontology of haecceities, properties like “being identical with X” which is unique for X and responsible for its individuation. This is achieved in two steps. In the first half of the thesis (Chapters 2 to 5), the nature of the Problem of Distinction is clarified and Principles of Evaluations of the solution to the Problem of Distinction are set out. Then based on these Principles, the thesis argues against the main extant non-haecceity solutions to the Problem of Distinction including the Spacetime Points Solution, Bare Particularism, Trope Theory, and the Universal Bundle Theory. In the second half of the thesis (Chapters 6 to 9), it develops a novel ontology of haecceities. A Haecceity Mereology with three rules is proposed. According to this ontology, the reality is constituted by two fundamental kinds of properties, universals and haecceities. An individual substance is a special mereological sum of a haecceity and its correspondent universals. Hence, there are two distinct substances because of the distinction of two haecceities. Besides solving the Problem of Distinction, the ontology of haecceities also explains many other things such as the unity of substances. Further, we argue that, although our knowledge of substances is epistemically fallible, the relationship between a haecceity and its correspondent universals is metaphysically necessary

A general cognitive framework for context-aware systems: extensions and applications for high level information fusion approaches

Mención Internacional en el título de doctorContext-aware systems aims at the development of computational systems that process data acquired from different datasources and adapt their behaviour in order to provide the 'right' information, at the 'right' time, in the 'right' place, in the 'right' way to the 'right' person (Fischer, 2012). Traditionally computational research has tried to answer these needs by means of low-level algorithms. In the last years the combination of numeric and symbolic approaches has offered the opportunity to create systems to deal with these issues. However, although the performance of algorithms and the quality of the data directly provided by computers and devices has quickly improved, symbolic models used to represent the resulting knowledge have not yet been adapted to smart environments. This lack of representation does not allow to take advantage of the semantic quality of the information provided by new sensors. This dissertation proposes a set of extensions and applications focused on a cognitive framework for the implementation of context-aware systems based on a general model inspired by the Information Fusion paradigm. This model is stepped in several abstraction levels from low-level raw data to high level scene interpretation whose structure is determined by a set of ontologies. Each ontology level provides a skeleton that includes general concepts and relations to describe entities and their connections. This structure has been designed to promote extensibility and modularity, and might be refined to apply this model in specific domains. This framework combines a priori context knowledge represented with ontologies with real data coming from sensors to support logic-based high-level interpretation of the current situation and to automatically generate feedback recommendations to adjust data acquisition procedures. This work advocates for the introduction of general purpose cognitive layers in order to obtain a closer representation to the human cognition, generate additional knowledge and improve the high-level interpretation. Extensibility and adaptability of the basic ontology levels is demonstrated with the introduction of these traverse semantic layers which are able to be present and represent information at several granularity levels of knowledge using a common formalism. Context-based system must be able to reason about uncertainty. However the reasoning associated to ontologies has been limited to classical description logic mechanisms. This research also tackle the problem of reasoning under uncertainty circumstances through a logic-based paradigm for abductive reasoning: the Belief-Argumentation System. The main contribution of this dissertation is the adaptation of the general architecture and the theoretical proposals to several context-aware application areas such as Ambient Intelligence, Social Signal Processing and surveillance systems. The implementation of prototypes and examples for these areas are explained along this dissertation to progressively illustrate the improvements and extensions in the framework. To initially depict the general model, its components and the basic reasoning mechanisms a video-based Ambient Intelligence application is presented. The advantages and features of the framework extensions through traverse cognitive layers are demonstrated in a Social Signal Processing case for the elaboration of automatic market researches. Finally, the functioning of the system under uncertainty circumstances is illustrated with several examples to support decision makers in the detection of potential threats in common harbor scenarios.Programa Oficial de Doctorado en Ciencia y Tecnología InformáticaPresidente: José Manuel Molina López.- Secretario: Ángel Arroyo.- Vocal: Nayat Sánchez P