http://hdl.handle.net/11089/57695 Sun, 05 Apr 2026 21:07:24 GMT 2026-04-05T21:07:24Z http://hdl.handle.net/11089/57698 Semi-Substructural Logics à la Lambek with Symmetry Wan, Cheng-Syuan This work studies the proof theory and ternary relational semantics of left (right) skew monoidal closed categories and skew monoidal bi-closed categories, both symmetric and non-symmetric, from the perspective of non-associative Lambek calculus. Uustalu et al. used sequents with stoup (the leftmost position of an antecedent that can be either empty or a single formula) to deductively model left skew monoidal closed categories, yielding results regarding proof identities and categorical coherence. However, their syntax does not work well when modeling right skew monoidal closed and skew monoidal bi-closed categories, whether symmetric or non-symmetric.We solve the problem via more flexible and equivalent frameworks to characterize the categories above: tree sequent calculus (where antecedents are binary trees) and axiomatic calculus (where antecedents are a single formula), inspired by works on non-associative Lambek calculus. Moreover, we prove that the axiomatic calculi are sound and complete with respect to their ternary relational models. We also prove a correspondence between frame conditions and structural laws, providing an algebraic way to understand the relationship between the left and right skew monoidal closed categories, encompassing both symmetric and non-symmetric variants. Fri, 13 Mar 2026 00:00:00 GMT http://hdl.handle.net/11089/57698 2026-03-13T00:00:00Z http://hdl.handle.net/11089/57700 Agent-Knowledge Logic for Alternative Epistemic Logic Nishimura, Yuki Epistemic logic is known as a logic that captures the knowledge and beliefs of agents and has undergone various developments. In this paper, we propose a new logic called agent-knowledge logic by taking the product of individual knowledge structures and the set of relationships among agents. This logic is based on the Facebook logic and the Logic of Hide and Seek Game. We show two main results; one is that this logic can embed the standard epistemic logic, and the other is that there is a proof system of tableau calculus that works in finite time. We also discuss various sentences and inferences that this logic can express. Fri, 13 Mar 2026 00:00:00 GMT http://hdl.handle.net/11089/57700 2026-03-13T00:00:00Z http://hdl.handle.net/11089/57699 Complexity of Nonassociative Lambek Calculus with Classical and Intuitionistic Logic Płaczek, Paweł The Nonassociative Lambek Calculus (NL) represents a logic devoid of the structural rules of exchange, weakening, and contraction, and it does not presume the associativity of its connectives. Its finitary consequence relation is decidable in polynomial time. However, the addition of classical connectives conjunction and disjunction (FNL) makes the consequence relation undecidable. Interestingly, if these connectives are distributive, the consequence relation is decidable in exponential time. This paper provides the proof, that we can merge classical logic with NL (i.e. BFNL) and intuitionistic logic with NL (i.e. HFNL), and still consequence relations are decidable in exponential time. Fri, 13 Mar 2026 00:00:00 GMT http://hdl.handle.net/11089/57699 2026-03-13T00:00:00Z http://hdl.handle.net/11089/57697 Qualified Definiteness Więckowski, Bartosz According to Russell, the definite article ‘the’ in a definite description ‘the F’ is used strictly in case there is a unique F and it is used loosely in case there is more than one F. Russell’s analysis of constructions of the form ‘the F is G’ is concerned only with the strict use. We modify this analysis so as to allow also for the loose use. This is achieved essentially by replacing the usual undefined notion of identity in Russell’s uniqueness clause with the defined notion of qualified identity (i.e., ‘a is the same as b in all Q-respects’, where Q is a subset of the set of predicate constants P) proposed in earlier work. This modification gives us qualified notions of uniqueness and definiteness. A qualified definiteness statement ‘the Q-unique F is G’ is strict in case Q=P and loose in case Q is a proper subset of P. The account is made formally precise in terms of proof theory and proof-theoretic semantics. The framework is intended to be acceptable from a foundational intuitionistic point of view. It is applied to natural language constructions with complete, incomplete, and generic definite descriptions. Also constructions with nested and with predicatively used definite descriptions are considered as well as constructions involving possessives. This work incorporates and extends my NCL’24-paper ‘Incomplete descriptions and qualified definiteness’. Fri, 13 Mar 2026 00:00:00 GMT http://hdl.handle.net/11089/57697 2026-03-13T00:00:00Z