Axioms vs Hypersequent Rules with Context Restrictions: Theory and Applications
نویسنده
چکیده
We introduce transformations between hypersequent rules with context restrictions and Hilbert axioms extending classical (and intuitionistic) propositional logic and vice versa. The introduced rules are used to prove uniform cut elimination, decidability and complexity results as well as finite axiomatisations for many modal logics given by simple frame properties. Our work subsumes many logic-tailored results and allows for new results. As a case study we apply our methods to the logic of uniform deontic frames.
منابع مشابه
Hypersequent and Labelled Calculi for Intermediate Logics
Hypersequent and labelled calculi are often viewed as antagonist formalisms to define cut-free calculi for non-classical logics. We focus on the class of intermediate logics to investigate the methods of turning Hilbert axioms into hypersequent rules and frame conditions into labelled rules. We show that these methods are closely related and we extend them to capture larger classes of intermedi...
متن کاملBunched Hypersequent Calculi for Distributive Substructural Logics
We introduce a new proof-theoretic framework which enhances the expressive power of bunched sequents by extending them with a hypersequent structure. A general cut-elimination theorem that applies to bunched hypersequent calculi satisfying general rule conditions is then proved. We adapt the methods of transforming axioms into rules to provide cutfree bunched hypersequent calculi for a large cl...
متن کاملTranslating Labels to Hypersequents for Intermediate Logics with Geometric Kripke Semantics
We give a procedure for translating geometric Kripke frame axioms into structural hypersequent rules for the corresponding intermediate logics in Int/Geo that admit weakening, contraction and in some cases, cut. We give a procedure for translating labelled sequents in the corresponding logic to hypersequents that share the same linear models (which correspond to Gödel-Dummett logic). We prove t...
متن کاملOn the Difference between Bridge Rules and Lifting Axioms
In a previous paper, we proposed a first formal and conceptual comparison between the two most important formalizations of context in AI: Propositional Logic of Context (PLC) and Local Models Semantics/MultiContext Systems (LMS/MCS). The result was that LMS/MCS is at least as general as PLC, as it can be embedded into a particular class of MCS, called MPLC. In this paper we go beyond that resul...
متن کاملBasic Paramodulation
We introduce a class of restrictions for the ordered paramodulation and superposition calculi (inspired by the basic strategy for narrowing), in which paramodulation inferences are forbidden at terms introduced by substitutions from previous inference steps. In addition we introduce restrictions based on term selection rules and redex orderings, which are general criteria for delimiting the ter...
متن کامل