Aristotle’s assertoric syllogistic and modern relevance logic

This paper sets out to evaluate the claim that Aristotle’s Assertoric Syllogistic is a relevance logic or shows significant similarities with it. I prepare the grounds for a meaningful comparison by extracting the notion of relevance employed in the most influential work on modern relevance logic, Anderson and Belnap’s Entailment. This notion is characterized by two conditions imposed on the concept of validity: first, that some meaning content is shared between the premises and the conclusion, and second, that the premises of a proof are actually used to derive the conclusion. Turning to Aristotle’s Prior Analytics, I argue that there is evidence that Aristotle’s Assertoric Syllogistic satisfies both conditions. Moreover, Aristotle at one point explicitly addresses the potential harmfulness of syllogisms with unused premises. Here, I argue that Aristotle’s analysis allows for a rejection of such syllogisms on formal grounds established in the foregoing parts of the Prior Analytics. In a final section I consider the view that Aristotle distinguished between validity on the one hand and syllogistic validity on the other. Following this line of reasoning, Aristotle’s logic might not be a relevance logic, since relevance is part of syllogistic validity and not, as modern relevance logic demands, of general validity. I argue that the reasons to reject this view are more compelling than the reasons to accept it and that we can, cautiously, uphold the result that Aristotle’s logic is a relevance logic

Cladonia rangiferina F. H. Wigg

<i>3.3. Proposed polyketide synthesis in Cladonia rangiferina</i> <p> A pervious study (Elshobary et al., 2016) showed that <i>CrPKS1</i> and <i>CrPKS16</i> may be genes that encode non-reducing enzymes and <i>CrPKS3</i> may encode a reducing enzyme. Furthermore, <i>CrPKS1</i> was most closely related to the putative <i>PKS</i> from <i>Pyrenophora tritici-repentis</i> (Diedicke) Drechsler and <i>Macrophomina phaseolina</i> (Tassi) Goidanich (both with maximum identity of 78 and 79%, respectively), which were responsible for production of 6-methylsalicylic acid synthase. The 6-methylsalicylic acid is considered the first cyclic compound in the polyketide pathway and a common precursor for the cyclic polyketide compounds (Legaz et al., 2011). Alternatively, the <i>C. grayi PKS1</i> (<i>CgPKS1</i>) (similarity with <i>CrPKS1</i> was 99% identity) was shown to fall within a phylogenetic clade that had a methyltransferase domain (Armaleo et al., 2011) suggesting it may produce the first cyclic compound (methyl-3-orsellinate) in the atranorin and fumarprotocetraric acid pathway (Fig. 4). Accordingly, <i>CrPKS1</i> is expected to be highly expressed in the thallus outer layer where the acetate/malonate and cyclisation presumably occur after transportation of algal sugars.</p> <p> <i>CrPKS16</i> was most closely related to the putative <i>PKS</i> from <i>C. grayi</i> (<i>CgPKS16</i>; maximum identity of 100%) which was hypothesized to be responsible for the synthesis and linking of two cyclic compounds <b>(</b> Methyl-3-orsellinate and sphaerophorolcarboxylic acid) to produce the grayanic acid precursor (4-O-demethylsphaerophorin; Fig. 5A) (Armaleo et al., 2011). Both 4-O-demethylsphaerophorin and atranorin are similar depsides except in the side chain at C 16 and the methylated carboxyl group (Fig. 5). Accordingly, <i>CrPKS16</i> may be involved in the linkage of two cyclic compounds (Methyl-3-orsellinate and Haemmatomoyl alcohol) to form atranorin (Fig. 5B). <i>CrPKS16</i> was expressed in both the outer and inner thallus tissue, which was consistent with the TLC data showing atranorin in both layers. However, the transformation of depsides to depsidones requires cytochrome P450 to form grayanic acid from depside precursors (Armaleo et al., 2011). In this context, Elix and Stocker-Wörgötter (2008) and Millot et al. (2009) suggested that a depsidone could be formed from the oxidation of a para-depside by dioxygenase. If depsides can be converted to depsidones (Seshadri, 1944; Culberson, 1964), the production of fumarprotocetraric acid in <i>C. rangiferina</i> may initially require the production of atranorin (Fig. 6) (de Armas et al., 2016). In this study, grayanic acid was not produced by <i>C. rangiferina</i>, so <i>CrPKS16</i> likely does not have a role in grayanic acid production. It may, instead, contribute to the biosynthesis of the depside, atranorin. This agreed, in part, with our TLC results which showed fumarprotocetraric acid present in the inner thallus layer with atranorin. If atranorin was formed in the outer layer and then transformed to fumarprotocetraric acid in the inner layer by dioxygenase (YQE1), which was upregulated in this layer, atranorin would appear to be present in both layers, and only fumarprotocetraric acid would appear to be present in the inner layer. However, the absence of <i>YQE1</i> expression in the apical inner layer does not support this hypothesis. <i>CrPKS3</i> was closely related to a reducing PKS gene from <i>Usnea longissima</i> Ach. (maximum identity of 74%) which may be responsible for the biosynthesis of depside side chains (Wang et al., 2011). This agreed with our results which showed that <i>CrPKS3</i> was more highly expressed in the outer than inner thallus layers where depside synthesis occurred.</p> <p> The Mass Spectrum analysis of atranorin (pure and in the extract) was consistent with previous reports (Musharraf et al., 2015) displaying the deprotonated molecular ion [M− H]− at m/z 373 with daughter ions observed at m/z 195 and 177 (Supplementary Fig. 1A, insert). Similarly, fumarprotocetraric acid had a [M− H]− precursor m/z 471 (both pure and in extract) in agreement with MoNA (MoNA ID: NP_C1_297_p3_F03_NEG_iTree_11), with the daughter ion observed at m/z 355 (Splash: splash10-0a4i-0009000000-6d53e7820a534e1cad6a) (Fig. 1B, insert). The analysis of both standards and published data strongly suggest the presence of atranorin and fumarprotocetraric acid as the two major compounds produced by <i>Cladonia rangiferina</i>.</p> <p> <b>4. Conclusion</b></p> <p> In conclusion, the three PKS genes (<i>CrPKS1</i>, <i>CrPKS3, CrPKS16)</i>, <i>MFSUG2</i>, and C 2 H 2 transcription factors were upregulated in the outer apical portion more than the other thallus portions. These findings are consistent with more metabolic activity where the ribitol sugar from the alga (<i>Asterochloris</i> sp.) is transferred to the fungus for polyketide production. However, the C 2 H 2 transcription factor was upregulated in both apical portions where polyketides were synthesized. In contrast, <i>PacC</i> was upregulated in the basal portion distal from polyketide synthesis. <i>YQE1</i> was upregulated in the basal inner layer where fumarprotocetraric acid biosynthesis may occur by oxidation of depsides. <i>CAT</i> was expressed in the outer layers of the thallus where polyketide biosynthesis initiated, which was thought to reduce the oxidative stress from polyketide biosynthesis. In contrast, the apothecia showed low expression levels of all genes. The results in this study are validated by current knowledge of sugar transport in lichens and the location of polyketide production consistent with known function. The utility of performing the LMD technique on sections of <i>C. rangiferina</i> has implications for further tissue-specific expression studies such as nitrogen mobilization in cyanobacterial lichens and it illustrates a different approach for examining activity of hydrophobins or other proteins in the lichen thallus.</p> 5. Materials and methods <p> <i>5.1. Lichen material</i></p> <p> The mat-forming lichen, <i>C. rangiferina</i> (L.) F. H. Wigg. (KP001201) was collected June 2014 from Sandilands Provincial Forest, Manitoba, Canada (N49̊ 22 <i>′</i> 37 <i>″</i>, W96̊ 6 <i>′</i> 31 <i>″</i>), cleaned from debris, and stored in a plastic bag at 4 ̊C. The collection site was a Jack pine (<i>Pinus banksiana</i> Lamb.) dominated ridge underlain by sandy glacial till on the Precambrian Shield. Other species present include black spruce (<i>Picea mariana</i> (Mill.) Britton, Sterns &Poggenb.), <i>Alnus</i> sp., <i>Prunus pensylvanica</i> L. in open areas, mosses (<i>Pleurozium schreberi</i> (Brid.) Mitt., <i>Hylocomium splendens</i> (Hedw.) Schimp., <i>Dicranum</i> spp.) in protected depressions, and other lichens (<i>Cladonia</i> spp., <i>Peltigera</i> spp.). See Kotelko et al. (2008) for a more detailed list of the common lichens and bryophytes in the area. The area was moist to dry with moisture retention because of the forest cover. The upper apical and lower basal portions of the lichen thallus were cut in cross section and separated into two layers: the outer layer with loose fungal hyphae surrounding algal cells and the innermost layer with compact fungal hyphae with no algal cells. The apothecia, containing only fungal tissue, were separated from the thallus at the base of the apothecium.</p>Published as part of <i>Elshobary, Mostafa E., Becker, Michael G., Kalichuk, Jenna L., Chan, Ainsley C., Belmonte, Mark F. & Piercey-Normore, Michele D., 2018, Tissue-specific localization of polyketide synthase and other associated genes in the lichen, Cladonia rangiferina, using laser microdissection, pp. 142-150 in Phytochemistry 156</i> on pages 145-147, DOI: 10.1016/j.phytochem.2018.09.011, <a href="http://zenodo.org/record/10484507">http://zenodo.org/record/10484507</a&gt