Algebraic and Proof-Theoretic Foundations of the Logics for Social Behaviour

This thesis is part of a line of research aimed at providing a strong and modular mathematical backbone to a wide and inherently diverse class of logics, introduced to capture different facets of social behaviour. The contributions of this thesis are rooted methodologically in duality, algebraic logic and structural proof theory, pertain to and advance three theories (unified correspondence, multi-type calculi, and updates on algebras) aimed at improving the semantic and proof-theoretic environment of wide classes of logics, and apply these theories to the introduction of logical frameworks specifically designed to capture concrete aspects of social behaviour, such as agents’ coordination and planning concerning the transformation and use of resources, and agents’ decision-making under uncertainty. The results of this thesis include: the characterization of the axiomatic extensions of the basic DLE-logics which admit proper display calculi; an algorithm computing the analytic structural rules capturing these axiomatic extensions; the introduction of a multi-type environment to describe and reason about agents’ abilities and capabilities to use and transform resources; the introduction of a proper display calculus for firstorder logic; the introduction of the intuitionistic counterpart of Probabilistic Dynamic Epistemic Logic, specifically designed to address situations in which truth is socially constructed. The results and methodologies developed in this thesis pave the way to the logical modelling of the inner workings of organizations and their dynamics, and of social phenomena such as reputational Matthew effects and bank runs.Ethics & Philosophy of Technolog

Modelling socio-political competition

This paper continues the investigation of the logic of competing theories (be they scientific, social, political etc.) initiated in [4]. We introduce a many-valued, multi-type modal language which we endow with relational semantics based on enriched reflexive graphs, inspired by Ploščica's representation of general lattices. We axiomatize the resulting many-valued, non-distributive modal logic of these structures and prove a completeness theorem. We illustrate the application of this logic through a case study in which we model competition among interacting political promises and social demands within an arena of political parties social groups

Toward an epistemic-logical theory of categorization

Categorization systems are widely studied in psychology, sociology, and organization theory as information-structuring devices which are critical to decision-making processes. In the present paper, we introduce a sound and complete epistemic logic of categories and agents' categorical perception. The Kripke-style semantics of this logic is given in terms of data structures based on two domains: one domain representing objects (e.g. market products) and one domain representing the features of the objects which are relevant to the agents' decision-making. We use this framework to discuss and propose logic-based formalizations of some core concepts from psychological, sociological, and organizational research in categorization theory.</p

Categories: How I Learned to Stop Worrying and Love Two Sorts

RS-frames were introduced by Gehrke as relational semantics for substructural logics. They are two-sorted structures, based on RS-polarities with additional relations used to interpret modalities. We propose an intuitive, epistemic interpretation of RS-frames for modal logic, in terms of categorization systems and agents’ subjective interpretations of these systems. Categorization systems are a key to any decision-making process and are widely studied in the social and management sciences. A set of objects together with a set of properties and an incidence relation connecting objects with their properties forms a polarity which can be ‘pruned’ into an RS-polarity. Potential categories emerge as the Galois-stable sets of this polarity, just like the concepts of Formal Concept Analysis. An agent’s beliefs about objects and their properties (which might be partial) is modelled by a relation which gives rise to a normal modal operator expressing the agent’s beliefs about category membership. Fixed-points of the iterations of the belief modalities of all agents are used to model categories constructed through social interaction

Toward an epistemic-logical theory of categorization

Categorization systems are widely studied in psychology, sociology, and organization theory as information-structuring devices which are critical to decision-making processes. In the present paper, we introduce a sound and complete epistemic logic of categories and agents' categorical perception. The Kripke-style semantics of this logic is given in terms of data structures based on two domains: one domain representing objects (e.g. market products) and one domain representing the features of the objects which are relevant to the agents' decision-making. We use this framework to discuss and propose logic-based formalizations of some core concepts from psychological, sociological, and organizational research in categorization theory.Ethics & Philosophy of Technolog