Deriving an Abstract Machine for Strong Call by Need

Strong call by need is a reduction strategy for computing strong normal forms in the lambda calculus, where terms are fully normalized inside the bodies of lambda abstractions and open terms are allowed. As typical for a call-by-need strategy, the arguments of a function call are evaluated at most once, only when they are needed. This strategy has been introduced recently by Balabonski et al., who proved it complete with respect to full beta-reduction and conservative over weak call by need. We show a novel reduction semantics and the first abstract machine for the strong call-by-need strategy. The reduction semantics incorporates syntactic distinction between strict and non-strict let constructs and is geared towards an efficient implementation. It has been defined within the framework of generalized refocusing, i.e., a generic method that allows to go from a reduction semantics instrumented with context kinds to the corresponding abstract machine; the machine is thus correct by construction. The format of the semantics that we use makes it explicit that strong call by need is an example of a hybrid strategy with an infinite number of substrategies

(Never) Mind your p's and q's: Von Neumann versus Jordan on the Foundations of Quantum Theory

In two papers entitled "On a new foundation [Neue Begr\"undung] of quantum mechanics," Pascual Jordan (1927b,g) presented his version of what came to be known as the Dirac-Jordan statistical transformation theory. As an alternative that avoids the mathematical difficulties facing the approach of Jordan and Paul A. M. Dirac (1927), John von Neumann (1927a) developed the modern Hilbert space formalism of quantum mechanics. In this paper, we focus on Jordan and von Neumann. Central to the formalisms of both are expressions for conditional probabilities of finding some value for one quantity given the value of another. Beyond that Jordan and von Neumann had very different views about the appropriate formulation of problems in quantum mechanics. For Jordan, unable to let go of the analogy to classical mechanics, the solution of such problems required the identication of sets of canonically conjugate variables, i.e., p's and q's. For von Neumann, not constrained by the analogy to classical mechanics, it required only the identication of a maximal set of commuting operators with simultaneous eigenstates. He had no need for p's and q's. Jordan and von Neumann also stated the characteristic new rules for probabilities in quantum mechanics somewhat differently. Jordan (1927b) was the first to state those rules in full generality. Von Neumann (1927a) rephrased them and, in a subsequent paper (von Neumann, 1927b), sought to derive them from more basic considerations. In this paper we reconstruct the central arguments of these 1927 papers by Jordan and von Neumann and of a paper on Jordan's approach by Hilbert, von Neumann, and Nordheim (1928). We highlight those elements in these papers that bring out the gradual loosening of the ties between the new quantum formalism and classical mechanics.Comment: New version. The main difference with the old version is that the introduction has been rewritten. Sec. 1 (pp. 2-12) in the old version has been replaced by Secs. 1.1-1.4 (pp. 2-31) in the new version. The paper has been accepted for publication in European Physical Journal

Problems, Puzzles, and Paradoxes for a Moral Psychology of Fiction

The goal of my dissertation is to provide a comprehensive account of our psychological engagements with fiction. While many aestheticians have written on issues concerning art and ethics, only a few have addressed the ways in which works of fiction offer problems for general accounts of morality, let alone how we go about making moral judgments about fictions in the first place. My dissertation fills that gap. I argue that the first challenge in explaining our interactions with fiction arises from functional and inferential arguments that entail that our mental states about fictional entities are non-genuine. This means that our mental states during our engagements with fiction are different in kind from typical beliefs, emotions, desires, etc. that we have in real-life contexts. I call this position the Distinct Attitude View (DAV). In its place, I propose a common-sense, standard attitude view (SAV): the idea that our psychological interactions with non-real entities can be explained in terms of the intentional content of those states as opposed to a distinct type of mental state. In expanding the SAV, I develop several independent accounts of social cognition, emotions, and moral judgments. I also show how the SAV can dissolve standard problems in the philosophy and psychology of aesthetic experience: the paradox of fiction, the problem of imaginative existence, and the sympathy for the devil phenomenon, amongst others

The Explication Defence of Arguments from Reference

In a number of influential papers, Machery, Mallon, Nichols and Stich have presented a powerful critique of so-called arguments from reference, arguments that assume that a particular theory of reference is correct in order to establish a substantive conclusion. The critique is that, due to cross-cultural variation in semantic intuitions supposedly undermining the standard methodology for theorising about reference, the assumption that a theory of reference is correct is unjustified. I argue that the many extant responses to Machery et al.’s critique do little for the proponent of an argument from reference, as they do not show how to justify the problematic assumption. I then argue that it can in principle be justified by an appeal to Carnapian explication. I show how to apply the explication defence to arguments from reference given by Andreasen (for the biological reality of race) and by Churchland (against the existence of beliefs and desires)

Probabilistic Argumentation with Epistemic Extensions and Incomplete Information

Abstract argumentation offers an appealing way of representing and evaluating arguments and counterarguments. This approach can be enhanced by a probability assignment to each argument. There are various interpretations that can be ascribed to this assignment. In this paper, we regard the assignment as denoting the belief that an agent has that an argument is justifiable, i.e., that both the premises of the argument and the derivation of the claim of the argument from its premises are valid. This leads to the notion of an epistemic extension which is the subset of the arguments in the graph that are believed to some degree (which we defined as the arguments that have a probability assignment greater than 0.5). We consider various constraints on the probability assignment. Some constraints correspond to standard notions of extensions, such as grounded or stable extensions, and some constraints give us new kinds of extensions

Asymptotic expansions for sums of block-variables under weak dependence

Let $\{X_i\}_{i=-\infty}^{\infty}$ be a sequence of random vectors and $Y_{in}=f_{in}(\mathcal{X}_{i,\ell})$ be zero mean block-variables where $\mathcal{X}_{i,\ell}=(X_i,...,X_{i+\ell-1}),i\geq 1$, are overlapping blocks of length $\ell$ and where $f_{in}$ are Borel measurable functions. This paper establishes valid joint asymptotic expansions of general orders for the joint distribution of the sums $\sum_{i=1}^nX_i$ and $\sum_{i=1}^nY_{in}$ under weak dependence conditions on the sequence $\{X_i\}_{i=-\infty}^{\infty}$ when the block length $\ell$ grows to infinity. In contrast to the classical Edgeworth expansion results where the terms in the expansions are given by powers of $n^{-1/2}$, the expansions derived here are mixtures of two series, one in powers of $n^{-1/2}$ and the other in powers of $[\frac{n}{\ell}]^{-1/2}$. Applications of the main results to (i) expansions for Studentized statistics of time series data and (ii) second order correctness of the blocks of blocks bootstrap method are given.Comment: Published at http://dx.doi.org/10.1214/009053607000000190 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Strong Admissibility Revisited (proofs)

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