Variable types for meaning assembly: a logical syntax for generic noun phrases introduced by most

This paper proposes a way to compute the meanings associated with sentences with generic noun phrases corresponding to the generalized quantifier most. We call these generics specimens and they resemble stereotypes or prototypes in lexical semantics. The meanings are viewed as logical formulae that can thereafter be interpreted in your favourite models. To do so, we depart significantly from the dominant Fregean view with a single untyped universe. Indeed, our proposal adopts type theory with some hints from Hilbert \epsilon-calculus (Hilbert, 1922; Avigad and Zach, 2008) and from medieval philosophy, see e.g. de Libera (1993, 1996). Our type theoretic analysis bears some resemblance with ongoing work in lexical semantics (Asher 2011; Bassac et al. 2010; Moot, Pr\'evot and Retor\'e 2011). Our model also applies to classical examples involving a class, or a generic element of this class, which is not uttered but provided by the context. An outcome of this study is that, in the minimalism-contextualism debate, see Conrad (2011), if one adopts a type theoretical view, terms encode the purely semantic meaning component while their typing is pragmatically determined

Modeling Nonintersective Adjectives Using Operator Logics

Our topic is one that involves the interface between natural language and mathematical logic. First-order predicate language/logic does a good job approximating many parts of (English) speech, i.e., nouns, verbs and prepositions, but fails decidedly when it comes to, say, adjectives. In particular, it cannot account for the quite different ways in which the adjectives green and big modify a noun such as chair. In the former case, we can easily view a world in which the class of green chairs is the intersection of the class of green things with the class of chair-things. By contrast, the way big modifies a noun depends on the noun itself: a big chair is microscopic when compared to the smallest of galaxies. We investigate logical languages inspired by this phenomenon; particularly those with variables ranging over individuals and with variable-binding operators akin to generalized quantifiers

Changing a semantics: opportunism or courage?

The generalized models for higher-order logics introduced by Leon Henkin, and their multiple offspring over the years, have become a standard tool in many areas of logic. Even so, discussion has persisted about their technical status, and perhaps even their conceptual legitimacy. This paper gives a systematic view of generalized model techniques, discusses what they mean in mathematical and philosophical terms, and presents a few technical themes and results about their role in algebraic representation, calibrating provability, lowering complexity, understanding fixed-point logics, and achieving set-theoretic absoluteness. We also show how thinking about Henkin's approach to semantics of logical systems in this generality can yield new results, dispelling the impression of adhocness. This paper is dedicated to Leon Henkin, a deep logician who has changed the way we all work, while also being an always open, modest, and encouraging colleague and friend.Comment: 27 pages. To appear in: The life and work of Leon Henkin: Essays on his contributions (Studies in Universal Logic) eds: Manzano, M., Sain, I. and Alonso, E., 201

Kolmogorov's Structure Functions and Model Selection

In 1974 Kolmogorov proposed a non-probabilistic approach to statistics and model selection. Let data be finite binary strings and models be finite sets of binary strings. Consider model classes consisting of models of given maximal (Kolmogorov) complexity. The ``structure function'' of the given data expresses the relation between the complexity level constraint on a model class and the least log-cardinality of a model in the class containing the data. We show that the structure function determines all stochastic properties of the data: for every constrained model class it determines the individual best-fitting model in the class irrespective of whether the ``true'' model is in the model class considered or not. In this setting, this happens {\em with certainty}, rather than with high probability as is in the classical case. We precisely quantify the goodness-of-fit of an individual model with respect to individual data. We show that--within the obvious constraints--every graph is realized by the structure function of some data. We determine the (un)computability properties of the various functions contemplated and of the ``algorithmic minimal sufficient statistic.''Comment: 25 pages LaTeX, 5 figures. In part in Proc 47th IEEE FOCS; this final version (more explanations, cosmetic modifications) to appear in IEEE Trans Inform T

The jet-disc connection: evidence for a reinterpretation in radio loud and radio quiet active galactic nuclei

To constrain models of the jet-disc connection, we explore Eddington ratios reported in Foschini (2011) and interpret them in relation to the values in Sikora et al. across the active galactic nuclei population from radio loud quasars, their flat spectrum radio quasar subclass, the recently discovered gamma-ray loud narrow-line type 1 Seyfert galaxies, Fanaroff-Riley type I (FRI) radio galaxies and radio quiet quasars of the Palomar Green survey. While appeal to disc truncation in radiatively inefficient flow appears to explain the observed inverse relation between radio loudness and Eddington ratio in radio loud and radio quiet quasars, FR I objects, scale invariance and recent data on powerful jets in narrow-line Seyfert 1 galaxies offer compelling arguments in favour of a reinterpretaion of the jet-disc connection