Object Exploration and a Problem with Reductionism

The purpose of this paper is to use neuroscientific evidence to address the philosophical issue of intertheoretic reduction. In particular, we present a literature review and a new experiment to show that the reduction of cognitive psychology to neuroscience is implausible. To make this case, we look at research using object exploration, an important experimental paradigm in neuroscience, behavioral genetics and psychopharmacology. We show that a good deal of object exploration research is potentially confounded precisely because it assumes that psychological generalizations can be reduced to neuroscientific ones.     

Some Properties of Orthologics

In this paper, we present three main results on orthologics. Firstly, we give a sufficient condition for an orthologic to have variable separation property and show that the orthomodular logic has this property. Secondly, we show that the class of modular orthologics has an infinite descending chain. Finally we show that there exists a continuum of orthologics.     

The Structure of the Ordinals and the Interpretation of ZF in Double Extension Set Theory

Andrzej Kisielewicz has proposed three systems of double extension set theory of which we have shown two to be inconsistent in an earlier paper. Kisielewicz presented an argument that the remaining system interprets ZF, which is defective: it actually shows that the surviving possibly consistent system of double extension set theory interprets ZF with Separation and Comprehension restricted to ₀ formulas. We show that this system does interpret ZF, using an analysis of the structure of the ordinals.     

Alan: An Action Language For Modelling Non-Markovian Domains

In this paper we present the syntax and semantics of a temporal action language named Alan, which was designed to model interactive multimedia presentations where the Markov property does not always hold. In general, Alan allows the specification of systems where the future state of the world depends not only on the current state, but also on the past states of the world. To the best of our knowledge, Alan is the first action language which incorporates causality with temporal formulas. In the process of defining the effect of actions we define the closure with respect to a path rather than to a state, and show that the non-Markovian model is an extension of the traditional Markovian model. Finally, we establish relationship between theories of Alan and logic programs.     

Admissibility of Cut in <Emphasis Type="Italic">LC</Emphasis> with Fixed Point Combinator

The fixed point combinator (Y) is an important non-proper combinator, which is defhable from a combinatorially complete base. This combinator guarantees that recursive equations have a solution. Structurally free logics (LC) turn combinators into formulas and replace structural rules by combinatory ones. This paper introduces the fixed point and the dual fixed point combinator into structurally free logics. The admissibility of (multiple) cut in the resulting calculus is not provable by a simple adaptation of the similar proof for LC with proper combinators. The novelty of our proof—beyond proving the cut for a newly extended calculus–is that we add a fourth induction to the by-and-large Gentzen-style proof. Presented by Robert Goldblatt