Monoidal computer III: A coalgebraic view of computability and complexity

Monoidal computer is a categorical model of intensional computation, where many different programs correspond to the same input-output behavior. The upshot of yet another model of computation is that a categorical formalism should provide a much needed high level language for theory of computation, flexible enough to allow abstracting away the low level implementation details when they are irrelevant, or taking them into account when they are genuinely needed. A salient feature of the approach through monoidal categories is the formal graphical language of string diagrams, which supports visual reasoning about programs and computations. In the present paper, we provide a coalgebraic characterization of monoidal computer. It turns out that the availability of interpreters and specializers, that make a monoidal category into a monoidal computer, is equivalent with the existence of a *universal state space*, that carries a weakly final state machine for any pair of input and output types. Being able to program state machines in monoidal computers allows us to represent Turing machines, to capture their execution, count their steps, as well as, e.g., the memory cells that they use. The coalgebraic view of monoidal computer thus provides a convenient diagrammatic language for studying computability and complexity.Comment: 34 pages, 24 figures; in this version: added the Appendi

Counting Incompossibles

We often speak as if there are merely possible people—for example, when we make such claims as that most possible people are never going to be born. Yet most metaphysicians deny that anything is both possibly a person and never born. Since our unreflective talk of merely possible people serves to draw non-trivial distinctions, these metaphysicians owe us some paraphrase by which we can draw those distinctions without committing ourselves to there being merely possible people. We show that such paraphrases are unavailable if we limit ourselves to the expressive resources of even highly infinitary first-order modal languages. We then argue that such paraphrases are available in higher-order modal languages only given certain strong assumptions concerning the metaphysics of properties. We then consider alternative paraphrase strategies, and argue that none of them are tenable. If talk of merely possible people cannot be paraphrased, then it must be taken at face value, in which case it is necessary what individuals there are. Therefore, if it is contingent what individuals there are, then the demands of paraphrase place tight constraints on the metaphysics of properties: either (i) it is necessary what properties there are, or (ii) necessarily equivalent properties are identical, and having properties does not entail even possibly being anything at all

Threats and challenges to the scientific representation of semantics: Carnap, Quine, and the Lessons of Semantic Skepticism

We will approach the problem of semantic skepticism by comparing Quine's view with Carnap's strategy for finding intensional equivalences that guarantee a solution to the paradox of analysis; and then we will consider how the Intensionalists use these possible solutions to save the scientificity of semantics. Quine disagrees with Carnap that plausible solutions to the question of intensional equivalence provide us with explanations for the difficult problems. These are ones where, in contrast to mere extensional indistinguishability of expressions, we need a stronger determination to choose the right interpretation. And then he has a skeptical answer to which the semanticist-linguist cannot remain insensitive. The problem is that a semanticist can only say that he has an "object" of inquiry if a normative property can be reconstructed, but that is not guaranteed by the mathematical theory used to infer intensional values. Finally, we would like to point out the relevance of skeptical doctrines about semantics that go beyond the mere haunting of relativism or quietism about meaning. Without a skeptical approach, we argue, we lose sight of the unique nature of language and its peculiar property of being an object shaped by pressures on its own ability to be theorized. &nbsp

\u27You\u27 Will Always Have \u27Me\u27: A Compositional Theory of Person

This dissertation investigates the morpho-syntactic makeup of personful expressionsin natural language; special focus is given to referential uses of personal pronouns. The central thesis guiding the inquiry is that utterance contexts, which serve to fix the semantic values of person indexicals, are specifically a kind of centered situation. This treatment of contexts puts restrictions on what kinds of person features are definable, and the resulting inventory of such features (in conjunction with independently-motivated pragmatic constraints on the use of referential expressions) provides a novel explanation for the typology of person systems

An Approach to Conceptual Schema Evolution

In this work we will analyse conceptual foundations of user centric content management. Content management often involves integration of content that was created from different points of view. Current modeling techniques and especially current systems lack of a sufficient support of handling these situations. Although schema integration is undecideable in general, we will introduce a conceptual model together with a modeling and maintenance methodology that simplifies content integration in many practical situations. We will define a conceptual model based on the Higher-Order Entity Relationship Model that combines advantages of schema oriented modeling techniques like ER modeling with element driven paradims like approaches for semistructured data management. This model is ready to support contextual reasoning based on local model semantics. For the special case of schema evolution based on schema versioning we will derive the compatibility relation between local models by tracking dependencies of schema revisions. Additionally, we will discuss implementational facets, such as storage aspects for structurally flexible content or generation of adaptive user interfaces based on a conceptual interaction model

Substructural Logics and Pragmatic Enrichment

In this dissertation, we argue for a Pragmatic Logical Pluralism, a pluralist thesis about logic which endorses Classical, Relevant, Linear, and Ordered logic. We justify that the formal languages of these four logics are legitimate codifications of the logical vocabulary and capture legitimate senses of logical consequence. This will be justified given a particular interpretation of the four formal languages: logical consequence and conditional, disjunction, and conjunction of the four different logics codify different and legitimate senses of ‘follows from’, ‘if...then’, ‘or’ and ‘and’ which diverge in their different pragmatic enrichments. The dissertation is twofold. First, we will explore the effect that the lack of structural rules has on logical connectives, in four substructural logics, and its connection with certain pragmatic enrichments. Second, we will defend a pluralist thesis according to which pragmatics has an important role for capturing the inferential role of logical vocabulary, both of the notions of ‘follows from’ and the logical constants, although classical logic preserves truth and captures their lit- eral meaning. In sum, we defend a version of logical pluralism based on the plurality of legitimate translations from natural language to formal languages, arguing that more than one translation is legitimate for logical vocabulary, which makes it possible to adopt more than one logic.En aquesta tesi presentem el Pluralisme Lògic Pragmàtic, una tesi pluralista sobre la lògica que accepta les lògiques Clàssica, Rellevant, Lineal i Ordenada. Justifiquem que els llenguatges formals d’aquestes quatre lògiques són codificacions legítimes del vocabulari lògic i capturen sentits legítims de la conseqüència lògica. Això es justificarà donant una interpretació particular dels quatre llenguatges formals: la conseqüència lògica i el condicional, la disjunció i la conjunció de les quatre lògiques acceptades codifiquen diferents i legítims sentits de ‘si...llavors’, ‘o’ i ‘i’, que es distingeixen pels diferents enriquiments pragmàtics que codifiquen. La tesi té dos vessants. Primer, explorem l’efecte que la falta de regles estructurals té en les connectives lògiques de les quatre lògiques presentades, i la seva connexió amb certs enriquiments pragmàtics. Segon, defensem una visió pluralista segons la qual la pragmàtica juga un rol important a l’hora de capturar el rol inferencial del vocabulari lògic, tant per la noció de conseqüència lògica com per les connectives, tot i que la lògica clàssica preserva la veritat i captura el seu significat literal. En resum, defensem una versió del pluralisme lògic basat en la pluralitat de traduccions legítimes del llenguatge natural al llenguatge formal, argumentant que més d’una traducció és legítima pel vocabulari lògic, la qual cosa ens permet adoptar més d’una lògica

Building Rules on Top of Ontologies for the Semantic Web with Inductive Logic Programming

Building rules on top of ontologies is the ultimate goal of the logical layer of the Semantic Web. To this aim an ad-hoc mark-up language for this layer is currently under discussion. It is intended to follow the tradition of hybrid knowledge representation and reasoning systems such as $\mathcal{AL}$-log that integrates the description logic $\mathcal{ALC}$ and the function-free Horn clausal language \textsc{Datalog}. In this paper we consider the problem of automating the acquisition of these rules for the Semantic Web. We propose a general framework for rule induction that adopts the methodological apparatus of Inductive Logic Programming and relies on the expressive and deductive power of $\mathcal{AL}$-log. The framework is valid whatever the scope of induction (description vs. prediction) is. Yet, for illustrative purposes, we also discuss an instantiation of the framework which aims at description and turns out to be useful in Ontology Refinement. Keywords: Inductive Logic Programming, Hybrid Knowledge Representation and Reasoning Systems, Ontologies, Semantic Web. Note: To appear in Theory and Practice of Logic Programming (TPLP)Comment: 30 pages, 6 figure