Propositional Relevance through Letter-Sharing: Review and Contribution

The concept of relevance between classical propositional formulae, defined in terms of letter-sharing, has been around for a very long time. But it began to take on a fresh life in 1999 when it was reconsidered in the context of the logic of belief change. Two new ideas appeared in independent work of Odinaldo Rodrigues and Rohit Parikh. First, the relation of relevance was considered modulo the belief set under consideration, Second, the belief set was put in a canonical form, known as its finest splitting. In this paper we explain these ideas; relate the approaches of Rodrigues and Parikh to each other; and briefly report some recent results of Kourousias and Makinson on the extent to which AGM belief change operations respect relevance. Finally we suggest a further refinement of the notion of relevance by introducing a parameter that allows one to take epistemic as well as purely logical components into account

Gödel’s Master Argument: what is it, and what can it do?

This text is expository. We explain Gödel’s ‘Master Argument’ for incompleteness as distinguished from the 'official' proof of his 1931 paper, highlight its attractions and limitations, and explain how some of the limitations may be transcended by putting it in a more abstract form that makes no reference to truth

Boole's indefinite symbols re-examined

We show how one can give a clear formal account of Boole’s notorious “indefinite" (or “auxiliary”) symbols by treating them as variables that range over functions from classes to classes rather than just over classes while, at the same time, following Hailperin’s proposal of binding them existentially

Tidal currents and vertical mixing processes beneath Filchner-Ronne ice shelf

Oceanographic measurements have been undertaken at sites on Filchner-Ronne Ice Shelf using hot-water drilled holes allowing conductivity-temperature-depth profiling and the deployment of instrument moorings. The data show that Western Shelf Water enters the sub-ice shelf cavity and occupies the lower portion of the water column. This is the water that provides the external heat necessary for melting within the sub-ice shelf cavity. A depth-averaged tidal model of the region has been used to show that in areas with shallow water and large topographic gradients, tidal oscillations with peak velocities up to 1 m s-1 play a significant role in the vertical mixing and transport of water masses. The estimated energy dissipation beneath Filchner-Ronne Ice Shelf resulting from surface friction is 25 GW, approximately 1% of the world’s total tidal dissipation. The model indicates that Lagrangian tidal residual currents have fluxes of up to 250,000 m3 s-1 and speeds of over 5 cm s-1 along the ice front, with over 350,000 m3 s-1 being exchanged between the sub-ice shelf cavity and adjacent continental shelf. These currents are particularly efficient in ventilating the sub-ice shelf cavity within 150 km of Ronne Ice Front. Furthermore, a one-dimensional turbulence closure ocean model has been applied to this sub-ice shelf environment which significantly lies near the critical latitude for the semi-diurnal tide. Here, the Coriolis frequency equals the tidal frequency, resulting in a strong depth dependent tidal current and thick boundary layers. Both the model and observations show that stratification significantly affects how the shape of the tidal current ellipse varies with depth. The model also shows that vertical mixing and basal melting are sensitive to tidal ellipse polarization with anticlockwise rotating tidal currents maintaining the highest melt rates. This sensitivity is due, in large part, to the proximity of the critical latitude

Relevance via decomposition: A project, some results, an open question

We report on progress and an unsolved problem in our attempt to obtain a clear rationale for relevance logic via semantic decomposition trees. Suitable decomposition rules, constrained by a natural parity condition, generate a set of directly acceptable formulae that contains all axioms of the well-known system R, is closed under substitution and conjunction, satisfies the letter-sharing condition, but is not closed under detachment. To extend it, a natural recursion is built into the ocedure for constructing decomposition trees. The resulting set of acceptable formulae has many attractive features, but it remains an open question whether it continues to satisfy the crucial letter-sharing condition

Relevance via decomposition

We report on progress and an unsolved problem in our attempt to obtain a clear rationale for relevance logic via semantic decomposition trees. Suitable decomposition rules, constrained by a natural parity condition, generate a set of directly acceptable formulae that contains all axioms of the well-known system R, is closed under substitution and conjunction, satisfies the letter-sharing condition, but is not closed under detachment. To extend it, a natural recursion is built into the procedure for constructing decomposition trees. The resulting set of acceptable formulae has many attractive features, but it remains an open question whether it continues to satisfy the crucial letter-sharing condition

Propositional relevance through letter-sharing

The concept of relevance between classical propositional formulae, defined in terms of letter-sharing, has been around for a long time. But it began to take on a fresh life in the late 1990s when it was reconsidered in the context of the logic of belief change. Two new ideas appeared in independent work of Odinaldo Rodrigues and Rohit Parikh: the relation of relevance was considered modulo the choice of a background belief set, and the belief set was put into a canonical form, called its finest splitting. In the first part of this paper, we recall the ideas of Rodrigues and Parikh, and show that they yield equivalent definitions of what may be called canonical cell/path relevance. The second part presents the main new result of the paper: while the relation of canonical relevance is syntax-independent in the usual sense of the term, it nevertheless remains language-dependent in a deeper sense, as is shown with an example. The final part of the paper turns to questions of application, where we present a new concept of parameter-sensitive relevance that relaxes the Rodrigues/Parikh definition, allowing it to take into account extra-logical sources as well as purely logical ones

Collective Decision-Making in Honey Bees during Nest-Site Selection

When a honey bee swarm leaves the colony it is faced with a tough dilemma; it must collectively locate, choose between and coordinate movement to the best quality nesting cavity it can find. The process of nest-site selection in the Western honey bee (Apis mellifera) is the best studied example of collective decision-making in the social insects. But A. mellifera is only one of eleven species within the genus Apis. Furthermore, the genus can be split into three categories based on nesting biology; cavity nesters (e.g. A. mellifera), dwarf open nesters (e.g A. florea) and giant open nesters (e.g. A. dorsata). Both open nesting groups are migratory, following seasonal nectar flows. Dwarf open nesters build small colonies on shrub and tree branches, while due to their size giant open nesters are limited to nesting on large smooth surfaces such as the branches of large trees. In this thesis I test whether differences in nesting biology influence the decision-making processes used by these species. Creating swarms of A. florea and A. dorsata I found that unlike A. mellifera, neither of these species go through a process of waggle dance decay. In contrast to A. mellifera, A. florea scout bees did not frequently leave the swarm surface to re-evaluate sites being danced for, while A. dorsata took off from the swarm surface regularly. My results demonstrate that the decision-making process of A. florea is the simplest within the genus, with the decision-making process of A. dorsata appearing to be intermediate between the quality independent process of A. florea and the quality dependent process of A. mellifera. By forcing A. mellifera swarms to the air prior to the final phase of their decision-making process I demonstrated that they are unable to successfully guide themselves. My results suggest that quorum detection plays an important role in priming scouts to become swarm guides

On principles and problems of defeasible inheritance

We have two aims here: First, to discuss some basic principles underlying different approaches to Defeasible Inheritance; second, to examine problems of these approaches as they already appear in quite simple diagrams. We build upon, but go beyond, the discussion in the joint paper of Touretzky, Horty, and Thomason: A Clash of Intuitions

What is Input/Output Logic? Input/Output Logic, Constraints, Permissions

We explain the {em raison d\u27^etre} and basic ideas of input/output logic, sketching the central elements with pointers to other publications for detailed developments. The motivation comes from the logic of norms. Unconstrained input/output operations are straightforward to define, with relatively simple behaviour, but ignore the subtleties of contrary-to-duty norms. To deal with these more sensitively, we constrain input/output operations by means of consistency conditions, expressed via the concept of an outfamily. They also provide a convenient platform for distinguishing and analysing several different kinds of permission