Counterfactual attitudes and multi-centered worlds

Modality is traditionally defined as the expression of possibility or necessity. In English, modality is expressed by the modal auxiliaries such as can, would, should, or might; adjectives and adverbs such as possible, necessary, maybe, and absolutely; or phrasal verbs such as going to or have to. Theory of Mind (ToM) is broadly defined as the ability to attribute thoughts and beliefs to other people. ToM is usually expressed using propositional attitude verbs such as think as in Mary thinks that it will rain. Hegarty (2006, 2010) proposes that propositional attitude verbs are covertly modalized and can be analyzed using the same apparatus as modals. If this theory is correct, then attitude ascriptions that are used to express ToM should be acquired by children after the child has a command of modality. Previous research shows that modality emerges in children as young as two years of age (Choi, 1999), but that children do not reach adult proficiency until around twelve years of age (Coates, 1987). Similarly, ToM begins to emerge when children can pass the standard false belief task near their fourth birthday (Wimmer & Perner, 1983; Baron-Cohen, Leslie & Frith, 1985), but children lack the necessary interpretation of the thoughts and beliefs of other people until they are approximately twelve years old (Lalonde & Chandler, 2002). This study evaluates the acquisition of both modality and ToM in eighty-six first, third, and fifth graders, using elicitation tasks for modality and question-answer tasks to test for higher-order ToM. The data was then analyzed indicating the approximate age of the acquisition of different types of modality such as epistemic (both strong and weak), alethic, priority, and dynamic. These results were then compared to those of the ToM tasks which indicate the age at which first, second, third, and fourth order ToM are acquired. The data suggests that modality and ToM are interdependent. Based on the results, a strong sense of modality emerges before the appropriate use of expressions of the second-order ToM, and third and fourth order ToM are mastered before the more difficult expressions of modality.

Truth conditions of sentences ascribing non-doxastic propositional attitudes seem to depend on the information structure of the embedded clause. In this paper, we argue that this kind of sensitivity is a semantic phenomenon rather than a pragmatic one. We report four questionnaire studies which explore the impact of the information structure on the truth conditions of non-doxastic attitude ascriptions from different perspectives. The results of the first two studies show that the acceptability of those ascriptions can be affected by some structural modifications of the embedded clause, in particular, when we replace a simple form by an equivalent complex conjunctional form (‘p and q’). However, it is possible that different evaluations of such ascriptions have a pragmatic source, namely, the ascriptions with embedded conjunction imply that the agent’s attitude transfers to both conjuncts. In the second pair of studies, we further investigate the nature of this implication which can be classified as ‘Conjunction Elimination’ (CE) in the scope of an attitude verb. The results show that CE-inferences in the context of non-factive non-doxastic attitude ascriptions are not easily cancellable and hence of a semantic rather than pragmatic nature. The results are not conclusive when it comes to the factive non-doxastic attitudes. We conclude our findings by some considerations about a potential source of the observed difference between non-factive and factive attitude verbs and the significance of our general findings to the semantic theory of non-doxastic attitude ascriptions.

We present a quasienergy-based formulation of damped response theory where a common effective lifetime parameter has been introduced for all excited states in terms of complex excitation energies. The introduction of finite excited state lifetimes leads to a set of (complex) damped response equations, which have the same form to all orders in the perturbation. An algorithm is presented for solving the damped response equations in Hartree-Fock theory and Kohn-Sham density functional theory. The use of the quasienergy formulation allows us to obtain directly the computationally simplest expressions for damped response functions by applying a set of response parameter elimination rules, which minimize the total number of damped response equations to be solved. In standard response theory broadened absorption spectra are obtained by ad hoc superimposing lineshape functions onto the absorption stick spectra, whereas an empirical lineshape function common to all excitations is an integrated part of damped response theory. By superimposing the lineshape functions inherent in damped response theory onto the stick spectra of standard response theory, we show that the absorption spectra obtained in standard and damped response theory calculations are identical. We demonstrate that damped response theory may be applied to obtain absorption spectra in all frequency ranges, also those that are not readily addressed using standard response theory. This makes damped response theory an effective tool, e.g., for determining absorption spectra for large molecules, where the density of the excited states may be very high, and where standard response theory therefore is not applicable in practice. A thorough comparison is given between our formulation of damped response theory and the formulation by Norman et al. [J. Chem. Phys. 123, 194103 (2005)].

“The expression ‘free logic’ is an abbreviation for the phrase ‘free of existence assumptions with respect to its terms, general and singular’.”1 Classical quantification theory is not a free logic in this sense, since its standard formulations commonly assume that every singular term in every model is assigned a referent, an element of the universe of discourse. Indeed, since singular terms include not only singular constants, but also variables2, standard quantification theory may be regarded as involving even the assumption of the existence of the values of its variables, in accordance with Quine’s famous dictum: “to be is to be the value of a variable”3.

FREGE AND THE JUSTIFICATION OF LOGICAL LAWS In recent work on Frege, one of the most salient issues has been whether he was prepared to make serious use of semantic notions such as reference and truth. Those not familiar with this debate are often surprised to hear of it. Surely, they say, Frege's post-1891 writings are replete with uses of 'true' and 'refers'. But no one wants to deny that Frege makes use of such terms: Rather, what is at issue is how Frege understood them; more precisely, what is at issue is whether Frege employed them for anything like the purposes for which philosophers now employ them. What these purposes are, or should be, is itself a matter of philosophical dispute, and, although I shall discuss some aspects of this issue, my goal here is not to address it directly. My purpose here, rather - one of them, anyway - is to argue that Frege did make very serious use of semantic concepts: In particular, he offered informal mathematical arguments, making use of semantic notions, for semantic claims. For example, he argues that all of the axioms of the Begriffsschrift - the formal system in which he proves the basic laws of arithmetic - are true, that its rules of inference are truth-preserving, and that every well-formed expression in Begriffsschrift has been assigned a reference by the stipulations he makes about the references of its primitive expressions. Let me say at the outset that Frege was not Tarski and did not produce, as Tarski did, a formal semantic theory, a mathematical definition of truth. But that is not of any significance here. One does not have to provide a formal semantic theory to make serious use of semantic notions. At most, the question is whether Frege would have been prepared to offer such a theory, or whether he would have accepted the sort of theory Tarski provided (or some alternative), had he known of it. On the other hand, the issue is not whether Frege would have accepted Tarski’s theory of truth, or Godel ’ s proof that first-order logic is complete, as a piece of mathematics; it is whether he would have taken these results to have the kind of significance we (or at least some of us) would ascribe to them. Tarski’s argument in ‘The concept of truth in formalized languages’ shows that all axioms of the calculus of classes are true; the completeness theorem shows that every valid first-order schema is provable in certain formal systems.

Higher-order probabilistic programming languages allow programmers to write sophisticated models in machine learning and statistics in a succinct and structured way, but step outside the standard measure-theoretic formalization of probability theory. Programs may use both higher-order functions and continuous distributions, or even define a probability distribution on functions. But standard probability theory does not handle higher-order functions well: the category of measurable spaces is not cartesian closed. Here we introduce quasi-Borel spaces. We show that these spaces: form a new formalization of probability theory replacing measurable spaces; form a cartesian closed category and so support higher-order functions; form a well-pointed category and so support good proof principles for equational reasoning; and support continuous probability distributions. We demonstrate the use of quasi-Borel spaces for higher-order functions and probability by: showing that a well-known construction of probability theory involving random functions gains a cleaner expression; and generalizing de Finetti's theorem, that is a crucial theorem in probability theory, to quasi-Borel spaces.

Non-Abelian higher gauge theory has recently emerged as a generalization of standard gauge theory to higher-dimensional (two-dimensional in the present context) connection forms, and as such, it has been successfully applied to the non-Abelian generalizations of the Yang–Mills theory and 2-form electrodynamics. (2+1)-dimensional gravity, on the other hand, has been a fertile testing ground for many concepts related to classical and quantum gravity, and it is therefore only natural to investigate whether we can find an application of higher gauge theory in this latter context. In the present paper we investigate the possibility of applying the formalism of higher gauge theory to gravity in 2+1 dimensions, and we show that a nontrivial model of (2+1)-dimensional gravity coupled to scalar and tensorial matter fields — the ΣΦEA model — can be formulated as a higher gauge theory (as well as a standard gauge theory). Since the model has a very rich structure — it admits as solutions black-hole BTZ-like geometries, particle-like geometries as well as Robertson–Friedman–Walker cosmological-like expanding geometries — this opens a wide perspective for higher gauge theory to be tested and understood in a relevant gravitational context. Additionally, it offers the possibility of studying gravity in 2+1 dimensions coupled to matter in an entirely new framework.

The main argument of this paper is that language, like cognition, is basically intensional, i.e. expression of thoughts. The philosophical and logical consequences of this view are discussed and partly elaborated. The paper implies a fundamental critique of the study of language during the 20th century, which failed to recognize the essential cognitive (intensional) nature of language. A plea is made for a re-appraisal of late 19th century approaches in philosophy (e.g. Meinong, Stout), which are said to have been on the right track though lacking in formal precision. The 20th century extensional view of logic and language, which goes back to the early 1900s, is subjected to a fundamental critique. The intensional nature of language is shown to have far-reaching consequences for the theory of grammar and meaning. The formal grammatical and semantic theories developed during the 20th century from an extensional point of view are best seen as a prelude to more adequate intensional formal theories.

In this paper, we suggest a strategy for modelling cognitive context within a truth‐conditional semantics, using Asher's model of predication. This allows us to introduce the notion of type presupposition intended as a lexical constraint to the composition of the truth‐conditional content. More specifically, we suggest that this model of predication produces a notion of truth‐conditional meaning where the cognitive context fixes a set of lexical restrictions and forced modifications. We conclude that this model might offer an intermediate position between Minimalism and Contextualism: an account that provides intuitive truth conditions within a formal semantic theory.

Metaphor and formal semantic theory

Unlocking the complexity of phrasal composition: An interplay between semantic features and linguistic relations

In fluid theory, the kinetic equation is converted into a system of moment equations. Any wanted moment is thereby coupled with other moments in an infinite set of equations. In plasma kinetic theory, the linearized Fourier-transformed kinetic equation is solved for the distribution function, and the wanted moments are obtained afterward as functions of the electric field strength. A complete knowledge of the frequency and wavenumber electric field spectrum is needed for these moments to be determined as functions of t and r. This standard kinetic approach is not suitable beyond the weak turbulence limit, in which the interaction of waves is treated in the random phase approximation. In situations where regular structures in (t, r) space arise due to phase correlations, recourse is commonly taken to fluid theory. In the present paper the plasma kinetic theory is treated differently by taking the electric field not as the cause of the process to be studied, but as a mediator between different moments. An arbitrary number of moment equations can be obtained in this way. Only those that, in the fluid limit, pass over to the fluid equations will be used. Outside the fluid limit, these so-called kinetic transport equations represent a continuation of the fluid equations into the kinetic regime. One purpose of kinetic transport theory is to extend the plasma kinetic theory beyond the weak turbulence limit. In contrast to standard plasma kinetic theory, the formulation of kinetic transport theory allows an application to neutral gases by setting the particle charge to zero. Therefore a second purpose of kinetic transport theory is to extend the transport equations for neutral gases beyond the fluid limit and to define the transport coefficients for highly rarefied gases.

In this paper we explore how compositional semantics, discourse structure, and the cognitive states of participants all contribute to pragmatic constraints on answers to questions in dialogue. We synthesise formal semantic theories on questions and answers with techniques for discourse interpretation familiar from computational linguistics, and show how this provides richer constraints on responses in dialogue than either component can achieve alone.

Understanding language requires the ability to compose the meanings of words into phrase and sentence meanings. Formal theories in semantics have framed the hypothesis that all instances of meaning composition, irrespective of the syntactic and semantic properties of the expressions involved, boil down to a unique formal operation, that is, the application of a function to an argument, a view known as "Frege's Conjecture." We test the processing consequences of this idea using event-related potentials (ERPs) and a novel experimental paradigm where composition versus noncomposition of words from the same grammatical category (nouns) are compared in two different syntactic environments: predication and modification. We found that noun composition in a modification context, where the noun follows an adjective, elicits a reduced N400 component, whereas noun composition in a predication context, where the noun follows a verb, produces an enhanced LAN component. These data challenge the uniqueness thesis, central to formal semantics, and support instead linguistic theories and processing models that posit different composition operations for predicates and modifiers. (PsycInfo Database Record (c) 2020 APA, all rights reserved).

Standard perturbation theory (PT) and coupled mode theory (CMT) formulations fail or exhibit very slow convergence when applied to the analysis of geometrical variations in high index-contrast optical components such as Bragg fibers and photonic crystals waveguides. By formulating Maxwell's equations in perturbation matched curvilinear coordinates, we have derived several rigorous PT and CMT expansions that are applicable in the case of generic non-uniform dielectric profile perturbations in high index-contrast waveguides. In strong fiber tapers and fiber Bragg gratings we demonstrate that our formulation is accurate and rapidly converges to an exact result when used in a CMT framework even in the high index-contrast regime. We then apply our method to investigate the impact of hollow Bragg fiber ellipticity on its Polarization Mode Dispersion (PMD) characteristics for telecom applications. Correct PT expansions allowed us to design an efficient optimization code which we successfully applied to the design of dispersion compensating hollow Bragg fiber with optimized low PMD and very large dispersion parameter. We have also successfully extended this methodology to treat radiation scattering due to common geometric variations in generic photonic crystals. As an example, scattering analysis in strong 2D photonic crystal tapers is demonstrated.