# Substructural epistemic logics

@article{Sedlr2015SubstructuralEL, title={Substructural epistemic logics}, author={Igor Sedl{\'a}r}, journal={Journal of Applied Non-Classical Logics}, year={2015}, volume={25}, pages={256 - 285} }

The article introduces substructural epistemic logics of belief supported by evidence. The logics combine normal modal epistemic logics (implicit belief) with distributive substructural logics (available evidence). Pieces of evidence are represented by points in substructural models and availability of evidence is modelled by a function on the point set. The main technical result is a general completeness theorem. Axiomatisations are provided by means of two-sorted Hilbert-style calculi. It is…

## 16 Citations

### Substructural Logics for Pooling Information

- EconomicsLORI
- 2017

A generalization of the account of pooling information – offered by standard epistemic logic – based on intersection of sets of possible worlds based on information models for substructural logics and pooling is represented by fusion of information states is put forward.

### Epistemic extensions of substructural inquisitive logics

- PhilosophyJ. Log. Comput.
- 2021

A deductive system for the weakest epistemic inquisitive logic is described and completeness proved for this special case using the general method.

### Knowledge Is a Diamond

- Philosophy, Computer ScienceWoLLIC
- 2017

This paper proposes a formal semantics for substructural logics that allows to model knowledge on the basis of intuition, and overcomes some unintuitive features of the semantics from [3].

### Substructural Logics with a Reflexive Transitive Closure Modality

- PhilosophyWoLLIC
- 2017

Decidability and weak completeness are obtained for intuitionistic modal logic with the reflexive transitive closure box in the modal non-associative commutative full Lambek calculus with a simple negation.

### Weak relevant justification logics

- PhilosophyJournal of Logic and Computation
- 2022

This paper will develop ideas from [44]. We will generalize their work in two directions. First, we provide axioms for justification logics over the base logic B and show that the logic permits a…

### Relevant Reasoners in a Classical World

- Philosophy, Computer ScienceArXiv
- 2022

The main technical result of the paper is a modular completeness theorem parametrized by the relevant modal logic formalizing the agent’s reasoning.

### From positive PDL to its non-classical extensions

- MathematicsLog. J. IGPL
- 2019

A complete binary implicational axiomatization of the positive fragment of Propositional Dynamic Logic is provided to provide completeness proofs for non-classical extensions of positive PDL.

### SUBSTRUCTURAL INQUISITIVE LOGICS

- Philosophy, Computer ScienceThe Review of Symbolic Logic
- 2019

Any propositional logic that extends a basic substructural logic BSL (a weak, nondistributive, nonassociative, and noncommutative version of Full Lambek logic with a paraconsistent negation) can be enriched with questions in the style of inquisitive semantics and logic.

### Actual Issues for Relevant Logics

- PhilosophyErgo, an Open Access Journal of Philosophy
- 2020

I is common enough in work on relevant logics using Routley-Meyer frames to talk about a real world. This is naturally construed as the formal representative of the actual world. It is a natural…

### Tracking reasons with extensions of relevant logics

- PhilosophyLog. J. IGPL
- 2019

This paper demonstrates an affinity to these two approaches that suggests their pairing will provide good logics for tracking reasons in a fine-grained way and develops an analogy between the dot operator of justification logic and theory fusion in relevant logics.

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