Parallel Logical Inference

The inference capabilities of humans suggest that they might be using algorithms with high degrees of parallelism. This paper develops a completely parallel connectionist inference mechanism. The mechanism handles obvious inferences, where each clause is only used once, but may be extendable to harder cases

A Vernacular for Coherent Logic

We propose a simple, yet expressive proof representation from which proofs for different proof assistants can easily be generated. The representation uses only a few inference rules and is based on a frag- ment of first-order logic called coherent logic. Coherent logic has been recognized by a number of researchers as a suitable logic for many ev- eryday mathematical developments. The proposed proof representation is accompanied by a corresponding XML format and by a suite of XSL transformations for generating formal proofs for Isabelle/Isar and Coq, as well as proofs expressed in a natural language form (formatted in LATEX or in HTML). Also, our automated theorem prover for coherent logic exports proofs in the proposed XML format. All tools are publicly available, along with a set of sample theorems.Comment: CICM 2014 - Conferences on Intelligent Computer Mathematics (2014

Psychosemantic analyticity

It is widely agreed that the content of a logical concept such as and is constituted by the inferences it enters into. I argue that it is impossible to draw a principled distinction between logical and non-logical concepts, and hence that the content of non-logical concepts can also be constituted by certain of their inferential relations. The traditional problem with such a view has been that, given Quine’s arguments against the analytic-synthetic distinction, there does not seem to be any way to distinguish between those inferences that are content constitutive and those that are not. I propose that such a distinction can be drawn by appealing to a notion of ‘psychosemantic analyticity’. This approach is immune to Quine’s arguments, since ‘psychosemantic analyticity’ is a psychological property, and it is thus an empirical question which inferences have this property

Phase Space Transport in Noisy Hamiltonian Systems

This paper analyses the effect of low amplitude friction and noise in accelerating phase space transport in time-independent Hamiltonian systems that exhibit global stochasticity. Numerical experiments reveal that even very weak non-Hamiltonian perturbations can dramatically increase the rate at which an ensemble of orbits penetrates obstructions like cantori or Arnold webs, thus accelerating the approach towards an invariant measure, i.e., a near-microcanonical population of the accessible phase space region. An investigation of first passage times through cantori leads to three conclusions, namely: (i) that, at least for white noise, the detailed form of the perturbation is unimportant, (ii) that the presence or absence of friction is largely irrelevant, and (iii) that, overall, the amplitude of the response to weak noise scales logarithmically in the amplitude of the noise.Comment: 13 pages, 3 Postscript figures, latex, no macors. Annals of the New York Academy of Sciences, in pres

Tichý and Fictional Names

The paper examines two possible analyses of fictional names within Pavel Tichý’s Transparent Intensional Logic. The first of them is the analysis actually proposed by Tichý in his (1988) book The Foundations of Frege’s Logic. He analysed fictional names in terms of free variables. I will introduce, explain, and assess this analysis. Subsequently, I will explain Tichý’s notion of individual role (office, thing-to-be). On the basis of this notion, I will outline and defend the second analysis of fictional names. This analysis is close to the approach known in the literature as role realism (the most prominent advocates of this position are Nicholas Wolterstorff, Gregory Currie, and Peter Lamarque)

An Empirical Approach to Temporal Reference Resolution

This paper presents the results of an empirical investigation of temporal reference resolution in scheduling dialogs. The algorithm adopted is primarily a linear-recency based approach that does not include a model of global focus. A fully automatic system has been developed and evaluated on unseen test data with good results. This paper presents the results of an intercoder reliability study, a model of temporal reference resolution that supports linear recency and has very good coverage, the results of the system evaluated on unseen test data, and a detailed analysis of the dialogs assessing the viability of the approach.Comment: 13 pages, latex using aclap.st