In recent years, neuroimaging methods have been used to investigate how the human mind carries out deductive reasoning. According to some, the neural substrate of language is integral to deductive ...reasoning. According to others, deductive reasoning is supported by a language‐independent distributed network including left frontopolar and frontomedial cortices. However, it has been suggested that activity in these frontal regions might instead reflect non‐deductive factors such as working memory load and general cognitive difficulty. To address this issue, 20 healthy volunteers participated in an fMRI experiment in which they evaluated matched simple and complex deductive and non‐deductive arguments in a 2 × 2 design. The contrast of complex versus simple deductive trials resulted in a pattern of activation closely matching previous work, including frontopolar and frontomedial “core” areas of deduction as well as other “cognitive support” areas in frontoparietal cortices. Conversely, the contrast of complex and simple non‐deductive trials resulted in a pattern of activation that does not include any of the aforementioned “core” areas. Direct comparison of the load effect across deductive and non‐deductive trials further supports the view that activity in the regions previously interpreted as “core” to deductive reasoning cannot merely reflect non‐deductive load, but instead might reflect processes specific to the deductive calculus. Finally, consistent with previous reports, the classical language areas in left inferior frontal gyrus and posterior temporal cortex do not appear to participate in deductive inference beyond their role in encoding stimuli presented in linguistic format.
Abstract
Given the recent interest in the fragment of system $\mathbf{F}$ where universal instantiation is restricted to atomic formulas, a fragment nowadays named system ...${\mathbf{F}}_{\textbf{at}}$, we study directly in system $\mathbf{F}$ new conversions whose purpose is to enforce that restriction. We show some benefits of these new atomization conversions: (i) they help achieving strict simulation of proof reduction by means of the Russell–Prawitz embedding of $\textbf{IPC}$ into system $\mathbf{F}$, (ii) they are not stronger than a certain ‘dinaturality’ conversion known to generate a consistent equality of proofs, (iii) they provide the bridge between the Russell–Prawitz embedding and another translation, due to the authors, of $\textbf{IPC}$ directly into system ${\mathbf{F}}_{\textbf{at}}$ and (iv) they give means for explaining why the Russell–Prawitz translation achieves strict simulation whereas the translation into ${\mathbf{F}}_{\textbf{at}}$ does not.
This paper considers the problem of optimizing on-line the production scheduling of a multiple-line production plant composed of parallel equivalent machines which can operate at different speeds ...corresponding to different energy demands. The transportation lines may differ in length and the energy required to move the part to be processed along them is suitably considered in the computation of the overall energy consumption. The optimal control actions are recursively computed with Model Predictive Control aiming to limit the total energy consumption and maximize the overall production. Simulation results are reported to witness the potentialities of the approach in different scenarios.
•Advanced model based predictive control of manufacturing systems.•Dynamic modeling of manufacturing systems with Mixed Logical Dynamical models.•Receding Horizon (or Rolling Horizon) implementation with guaranteed due date.•Analysis of the performances and comparisons with Mixed Integer Linear Programming.
It follows from known results in the literature that least and greatest fixed-points of monotone polynomials on Heyting algebras—that is, the algebraic models of the Intuitionistic Propositional ...Calculus—always exist, even when these algebras are not complete as lattices. The reason is that these extremal fixed-points are definable by formulas of the
IPC
. Consequently, the μ-calculus based on intuitionistic logic is trivial, every μ-formula being equivalent to a fixed-point free formula. In the first part of this article, we give an axiomatization of least and greatest fixed-points of formulas, and an algorithm to compute a fixed-point free formula equivalent to a given μ-formula. The axiomatization of the greatest fixed-point is simple. The axiomatization of the least fixed-point is more complex, in particular every monotone formula converges to its least fixed-point by Kleene’s iteration in a finite number of steps, but there is no uniform upper bound on the number of iterations. The axiomatization yields a decision procedure for the μ-calculus based on propositional intuitionistic logic. The second part of the article deals with closure ordinals of monotone polynomials on Heyting algebras and of intuitionistic monotone formulas; these are the least numbers of iterations needed for a polynomial/formula to converge to its least fixed-point. Mirroring the elimination procedure, we show how to compute upper bounds for closure ordinals of arbitrary intuitionistic formulas. For some classes of formulas, we provide tighter upper bounds that, in some cases, we prove exact.
This paper studies the complexity of constant depth propositional proofs in the cedent and sequent calculus. We discuss the relationships between the size of tree-like proofs, the size of dag-like ...proofs, and the heights of proofs. The main result is to correct a proof construction in an earlier paper about transformations from proofs with polylogarithmic height and constantly many formulas per cedent.
Residuated basic logic (RBL) is the logic of residuated basic algebras, which constitutes a conservative extension of basic propositional logic (BPL). The basic implication is a residual of a ...non-associative binary operator in RBL. The conservativity is shown by relational semantics. A Gentzen-style sequent calculus GRBL, which is an extension of the distributive full non-associative Lambek calculus, is established for residuated basic logic. The calculus GRBL admits the mix-elimination, subformula, and disjunction properties. Moreover, the class of all residuated basic algebras has the finite embeddability property. The consequence relation of GRBL is decidable.
This brief describes the application of model predictive control to a manufacturing multipallet multitarget transport line. The mathematical representation of the plant is based on a mixed logical ...dynamical model. The performance index to be minimized weights the distance of the pallets from their final target, the pallet residence time on the line, and the control inputs. The resulting mixed integer linear programming problem is recursively solved to compute the control action according to the receding horizon approach. Both simulation and experimental results on the real system are reported and discussed to witness the performances of the control algorithm and its ability to manage even pallet route conflicts and target dynamic rescheduling.
PDF
