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PLEXUS. Philosophical, Logical, and Experimental Routes to Substructurality

Horizon Europe Framework Programme (HORIZON)

MSCA Staff Exchanges 2021 (HORIZON-MSCA-2021-SE-01)

There is a large family of non-classical logics that fall under the heading of substructurality. Since the first use of the term – around forty years ago – the interest of the scientific community in so-called substructural logics increased spectacularly. In effect, the search for «substructural logics» (quoting marks included) in Google Scholar renders around 4850 results distributed this way: 14 results between 1981 and 1990, 597 results between 1991 and 2000, 1450 between 2001 and 2010 and 2360 between 2011 and 2020. Among the logics in the substructural family, the recent philosophical literature pays particular attention to what can be termed “radical substructurality”: non-transitive and non-reflexive reflexive logics, as well as variants and hybrids of these obtained by metainferential ascent.

The overall goal of PLEXUS is to advance the knowledge of radically substructural logics and deepen our understanding of the broader phenomenon of substructurality, by coordinating the efforts of researchers across the globe, across generations, and across traditions. We see this project as characterised by the following concepts: integration, cross-fertilization and knowledge sharing.

Integration. Much of the research on substructural logics developed in a fragmented way by considering only some aspects of substructurality. This fragmentation was equally visible with respect to the philosophical motivations (the nature of logical consequence, pluralism, meaning of logical constants, applications to paradoxes and natural language phenomena) and the techniques employed for the analysis of logics (either model or proof oriented). In this project we seek to integrate these perspectives in the study of radical substructural logics.

Cross-fertilisation. The current research on non-transitive and non-reflexive substructural logics has led to a significant body of knowledge that is ready to be pushed to the next level by the cross-fertilization with knowledge in other disciplines. PLEXUS aims to take the first steps towards the design, validation and test of a psychometrical tool to measure naïve speakers’ preferences on structural rules as well as the implementation of theorem provers for radically substructural logics.

Knowledge sharing. PLEXUS will be a research network where ideas are transmitted at high speed from any point to any other point of the network, generating optimal conditions for a culture of research and innovation on substructural logics and for the training of a new generation of researchers in Europe and worldwide.

The overall goal of PLEXUS is articulated into three main research objectives:

Objective 1. Philosophical Foundations: PLEXUS will investigate the major philosophical challenges raised by non-transitive and non-reflexive substructural logics. In particular, we will investigate the nature of logical theories by addressing the paramount question of whether they are determined inferentially or metainferentially and, if the latter, whether this is done by a single metainferential level or by transfinite hierarchies of metainferences. In doing so, we will also evaluate different accounts of metainferential validity. Moreover, we will revisit legacy tenets such as the identification of sequents with claims of consequence and explore alternative views.

Objective 2. Logic: PLEXUS will advance knowledge of the field of substructural logics by developing new proof-theoretic and model-theoretic characterizations of radically substructural logics. We will develop both proof-theoretic calculi (e.g. hypersequents and labelled calculi) and model-theoretic techniques (including generalisations of the algebraic and model-theoretic characterizations of logics), to analyse the axiomatizations of substructural logics, and explore their meta-logical properties. In addition, we will systematically explore logico-linguistic applications of substructural logics, including theories of self-applicable truth, property instantiation, the logic of grounding, conditionals and models of reasonings under uncertainty.

Objective 3. The Metainferences Inventory & Metainferences Prover: PLEXUS seeks to design and validate a psychometric tool (i.e., the Metainferences Inventory) which would allow us to measure naïve speakers’ preferences on different questions about radical substructurality. We will focus on examining the psychometric properties of the tool (i.e., reliability and validity evidence) through different design phases. Complementary to this research, PLEXUS will extend existing techniques of automated reasoning to the logics covered by the project, focusing particularly on the decision of validity for metainferences.

The verification of the achievement of objectives 1 and 2 is linked principally to theoretical research outputs: (i) number and impact of scientific publications, (ii) number of participants in PLEXUS’ networking events and (iii) number of PhD thesis under the PLEXUS network. The verification of the achievement of objective 3 depends on the effective design and validation of the Metainferences Inventory and of the successful implementation of the Metainferences Prover – this objective should also lead to journal articles and related PhD thesis.

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