Information Flow in Logics in the Vicinity of BB

Situation theory, and channel theory in particular, have been used to provide motivational accounts of the ternary relation semantics of relevant, substructural, and various non-classical logics. Among the constraints imposed by channel-theory, we must posit a certain existence criterion for situations which result from the composites of multiple channels (this is used in modeling information flow). In associative non-classical logics, it is relatively easy to show that a certain such condition is met, but the problem is trickier in non-associative logics. Following Tedder (2017), where it was shown that the conjunction-conditional fragment of the logic B admits the existence of composite channels, I present a generalised ver- sion of the previous argument, appropriate to logics with disjunction, in the neighbourhood ternary relation semantic framework. I close by suggesting that the logic BB+(^I), which falls between Lavers' system BB+ and B+ , satisfies the conditions for the general argument to go through (and prove that it satisfies all but one of those conditions)

Information Flow in Logics in the Vicinity of BB

Situation theory, and channel theory in particular, have been used to provide motivational accounts of the ternary relation semantics of relevant, substructural, and various non-classical logics. Among the constraints imposed by channel-theory, we must posit a certain existence criterion for situations which result from the composites of multiple channels (this is used in modeling information flow). In associative non-classical logics, it is relatively easy to show that a certain such condition is met, but the problem is trickier in non-associative logics. Following Tedder (2017), where it was shown that the conjunction-conditional fragment of the logic B admits the existence of composite channels, I present a generalised ver- sion of the previous argument, appropriate to logics with disjunction, in the neighbourhood ternary relation semantic framework. I close by suggesting that the logic BB+(^I), which falls between Lavers' system BB+ and B+ , satisfies the conditions for the general argument to go through (and prove that it satisfies all but one of those conditions)

A Note on R-Mingle and the Danger of Safety

Dunn has recently argued that the logic R-Mingle (or RM) is a good, and good enough, choice for many purposes in relevant and paraconsistent logic. This includes an argument that the validity of Safety principle, according to which one may infer an arbitrary instance of the law of excluded middle from an arbitrary contradiction, in RM is not a problem because it doesn’t allow one to infer anything new from a contradiction. In this paper, I argue that while Dunn’s claim holds for the logic, there is a good reason to think that it’s not the case for (prime) theories closed under the logic, and that this should give relevantists, and some paraconsistentists, pause when considering whether RM is adequate for their purposes

Consistency and Decidability in Some Paraconsistent Arithmetics

The standard style of argument used to prove that a theory is unde- cidable relies on certain consistency assumptions, usually that some fragment or other is negation consistent. In a non-paraconsistent set- ting, this amounts to an assumption that the theory is non-trivial, but these diverge when theories are couched in paraconsistent logics. Furthermore, there are general methods for constructing inconsistent models of arithmetic from consistent models, and the theories of such inconsistent models seem likely to differ in terms of complexity. In this paper, I begin to explore this terrain, working, particularly, in incon- sistent theories of arithmetic couched in three-valued paraconsistent logics which have strong (i.e. detaching) conditionals

Consistency and Decidability in Some Paraconsistent Arithmetics

The standard style of argument used to prove that a theory is unde- cidable relies on certain consistency assumptions, usually that some fragment or other is negation consistent. In a non-paraconsistent set- ting, this amounts to an assumption that the theory is non-trivial, but these diverge when theories are couched in paraconsistent logics. Furthermore, there are general methods for constructing inconsistent models of arithmetic from consistent models, and the theories of such inconsistent models seem likely to differ in terms of complexity. In this paper, I begin to explore this terrain, working, particularly, in incon- sistent theories of arithmetic couched in three-valued paraconsistent logics which have strong (i.e. detaching) conditionals

A Note on R-Mingle and the Danger of Safety

Dunn has recently argued that the logic R-Mingle (or RM) is a good, and good enough, choice for many purposes in relevant and paraconsistent logic. This includes an argument that the validity of Safety principle, according to which one may infer an arbitrary instance of the law of excluded middle from an arbitrary contradiction, in RM is not a problem because it doesn’t allow one to infer anything new from a contradiction. In this paper, I argue that while Dunn’s claim holds for the logic, there is a good reason to think that it’s not the case for (prime) theories closed under the logic, and that this should give relevantists, and some paraconsistentists, pause when considering whether RM is adequate for their purposes

Comparing the consequences of mating system shifts between different species of cruciferous plants in relation to phylogeography.

Sporophytic self-incompatibility is a genetically controlled inbreeding prevention mechanism, which is prevalent in the Brassicaceae, and has been reported in a variety of high profile species. Despite the benefits of preventing self-fertilization in terms of maintaining genetic diversity, variation in the strength of self-incompatibility (SI) has also been well documented, as has a shift from SI to inbreeding at the species and population levels. An important underlying driving force behind a switch to inbreeding could be the reproductive assurance provided by not requiring an unrelated mating partner for sexual reproduction. This could be beneficial for a species undergoing rapid colonization, because only a single individual is required to begin a sexually reproducing colony after a long-distance dispersal event (Baker’s law), which is characteristic of the plight of many species after the last glacial maxima. The purpose of my thesis was to evaluate the effects of variation in mating system on post-glacial colonization, using two model species that show intraspecific variation in outcrossing rates. The first, Arabidopsis lyrata, represents an excellent model system to assess post-glacial colonization history because it exhibits broad geographical and ecological ranges, and has a recently completed genome sequence. In North America, A. lyrata has further benefits as a model system, namely it exhibits variation in the strength of SI and shift to SC at the population level, which is not observed in Europe. The second species is Arabis alpina, which also appears to show population level variation in mating system strength in Europe based on variation in FIS. This has been putatively linked to colonization history after the last glacial maxima. Unlike in A. lyrata however, its mating system has not been characterized. Mating system delimitation in A. alpina has the potential to aid the interpretation of patterns of ecological genetic diversity, which may in part be influenced by local or regional stochastic changes to mating system variation. My first objective was to identify if A. alpina had a functioning SI system based on both self-fertilization experiments, and allozyme based outcrossing rate estimations. I found strong evidence to suggest the presence of a functional barrier preventing self-fertilization in A. alpina. I identified multiple putative SRK alleles (the female determinant of self-incompatibility), suggesting that the same type of sporophytic system seen in other Brassicaceae species governs SI in this species. I also demonstrated linkage of SI phenotype to some SRK genotypes by diallel crosses, strengthening the case for a functional SI system in this species. Further to this I demonstrate variation in mating system strength between populations, and autonomous inbreeding was seen in a single population. I note that the potential changes in SI status coincide with areas suspected to differ in post-glacial history based on allozyme diversity reported in previous work. While the number of populations sampled was insufficient to link mating system variation to colonization history in A. alpina, mating system variation has been more extensively characterized in North American A. lyrata, allowing more fine-scale resolution of population structure and post-glacial colonization history; an underlying objective of my thesis. I used three molecular marker systems (cpDNA, nuclear micro-satellites and allozymes) to assess these phylogeographic questions, and present evidence of three putative colonization routes for the Great Lakes region. These putative routes are congruent with those described in other species, particularly amphibians and reptiles. Further to this I considered the possible location of glacial refugia, and likelihood that plant taxa may have survived during Pleistocene glaciation in close proximity to the Laurentide Ice Sheet, particularly in Illinois, Indiana, Wisconsin and Minnesota, which may also be true for some animal taxa. I examined patterns of population structure, and scenarios that may have influenced this, and present support for the previously documented theory of multiple breakdowns in SI in this geographic region. My final objective was to assess the suitability of the three marker systems for phylogeographic reconstruction in A. lyrata, by comparing and contrasting the patterns of population structure, and colonization history suggested by each system. Levels of variation observed between the marker systems used varied, and I explored how these patterns complemented and contradicted each other. As expected, the nuclear micro-satellite loci represent the system with the greatest genetic diversity, but do not allow meaningful conclusions to be drawn regarding colonization history because of low levels of shared variation between populations. Conversely, the allozyme loci presented much lower levels of genetic diversity, but support population structuring conclusions based on both cpDNA data and previous studies of A. lyrata and other taxa in this area. The cpDNA marker (trnF) represents a somewhat contentious system to use for phylogeography in A. lyrata, as it contains a tandem array of highly variable, but complexly evolving duplications (pseudogenes). I concluded that these structural changes could be phylogenetically informative when pseudogene evolutionary relationships can be resolved This was based on variation in patterns of diversity, and the subsequent population structure change that occurred when using different methods of assessing trnF variation