Proof-theoretic Semantics for Intuitionistic Multiplicative Linear Logic

This work is the first exploration of proof-theoretic semantics for a substructural logic. It focuses on the base-extension semantics (B-eS) for intuitionistic multiplicative linear logic (IMLL). The starting point is a review of Sandqvist’s B-eS for intuitionistic propositional logic (IPL), for which we propose an alternative treatment of conjunction that takes the form of the generalized elimination rule for the connective. The resulting semantics is shown to be sound and complete. This motivates our main contribution, a B-eS for IMLL , in which the definitions of the logical constants all take the form of their elimination rule and for which soundness and completeness are established

Microbial Habitability of Sulfate-rich Environments of Earth and Mars

Mars hosted ancient hypersaline sulfate lakes around 4 billion years ago in the early Noachian. Chemically similar environments on Earth are teeming with microbes that have adapted to these extreme conditions yet the microbiome of terrestrial MgSO4 systems has not yet been adequately constrained. This is essential in order to understand the potential habitability of epsomic environments of early Mars. This thesis presents the characterisation of the microbial community compositions of enrichments of epsomite (MgSO4.7H2O) crystals from Basque Lakes, British Columbia, Canada. Basque lakes are sulfate-rich playas that serve as analogues for Mars' ancient hypersaline sulfate lakes. The predominant microbial taxa, which are typically halophilic, are also epsotolerant, which means that they can grow at high MgSO4.7H2O concentrations but do not require it to grow. Microbes residing in such rare terrestrial epsomic habitats are exemplars of the putative microbial life deemed to be associated with equivalent environments on early Mars. Therefore, one of the major contributions of this thesis is that it adds to the inventory of model terrestrial halophiles that can help inform our understanding of viable metabolisms and potential biosignatures on Mars. This thesis also reports the discovery of three novel microbial species: two bacteria and one archaeon, isolated from Basque Lake epsomite enrichments and characterised through a suite of genomic, physiological, and chemotaxonomic tests. Four whole genome sequencing accession numbers granted by GenBank are also reported, with computational tools employed to assign functions to the genes in the novel isolates. The subsystem categories and gene clusters for metabolic and signalling pathways represented in the novel bacterial genomes could have a bearing on survival under oligotrophic as well as multiple physicochemical stresses. Given NASA’s and ESA’s robotic missions to Mars are currently targeting sulfate-rich environments the results of this thesis may inform the search for potentially habitable epsomitic niches on Mars that could host preserved biosignatures