On a curious property of 3435

Folklore tells us that there are no uninteresting natural numbers. But some natural numbers are more interesting then others. In this article we will explain why 3435 is one of the more interesting natural numbers around. We will show that 3435 is a Munchausen number in base 10, and we will explain what we mean by that. We will further show that for every base there are finitely many Munchausen numbers in that base.Comment: 5 pages, 1 table Added suggestions of Andrew Baxte

A Neutral Temporal Deontic STIT Logic

In this work we answer a long standing request for temporal embeddings of deontic STIT logics by introducing the multi-agent STIT logic TDS . The logic is based upon atemporal utilitarian STIT logic. Yet, the logic presented here will be neutral: instead of committing ourselves to utilitarian theories, we prove the logic TDS sound and complete with respect to relational frames not employing any utilitarian function. We demonstrate how these neutral frames can be transformed into utilitarian temporal frames, while preserving validity. Last, we discuss problems that arise from employing binary utility functions in a temporal setting

The Varieties of Ought-implies-Can and Deontic STIT Logic

STIT logic is a prominent framework for the analysis of multi-agent choice-making. In the available deontic extensions of STIT, the principle of Ought-implies-Can (OiC) fulfills a central role. However, in the philosophical literature a variety of alternative OiC interpretations have been proposed and discussed. This paper provides a modular framework for deontic STIT that accounts for a multitude of OiC readings. In particular, we discuss, compare, and formalize ten such readings. We provide sound and complete sequent-style calculi for all of the various STIT logics accommodating these OiC principles. We formally analyze the resulting logics and discuss how the different OiC principles are logically related. In particular, we propose an endorsement principle describing which OiC readings logically commit one to other OiC readings

An infrared investigation of the catalyst formation in the system Ni(acac)2, C3H4, (iBu)3AL for propadiene polymerization

The catalyst formation in the system Ni(acac)2, C3H4, (iBu)3Al was investigated by means of infrared spectroscopy. It was found that the Al(acac)3 and (iBu)2Al(acac) formed are both by-products of catalyst formation without a catalytic activity. Ni(acac)2 loses its acac groups forming the unstable (iBu)2Ni compound; without C3H4 being present, this compound disproportionates to Ni metal and isobutane and isobutene. In the presence of C3H4 an allyl-nickel complex is formed, which reacts with (iBu)3Al to give the actual catalyst, possibly a bimetallic allyl—nickel-aluminium complex. Catalysts such as Ni(acac)2, C3H4, (iBu)3Al and (πC3H5)2Ni with or without (iBu)3Al all selectively give 1, 2, 1, 2-polypropadiene. A Lewis base like pyridine not only decreases the polymerization rate but also changes the selectivity towards the formation of 1, 2, 2, 1-polymer