Related papers: Merging fragments of classical logic

We exhaustively classify varieties of BL-algebras with the amalgamation property, showing that there are only countably many of them and solving an open problem of Montagna. As a consequence of this classification, we obtain a complete…

This paper presents a range of quantitative extensions for the temporal logic CTL. We enhance temporal modalities with the ability to constrain the number of states satisfying certain sub-formulas along paths. By selecting the combinations…

We develop a framework for epistemic logic that combines relevant modal logic with classical propositional logic. In our framework the agent is modeled as reasoning in accordance with a relevant modal logic while the propositional fragment…

We study counting propositional logic as an extension of propositional logic with counting quantifiers. We prove that the complexity of the underlying decision problem perfectly matches the appropriate level of Wagner's counting hierarchy,…

Recently, arXiv:2312.16035 showed that all logics based on Boolean Normal monotonic three-valued schemes coincide with classical logic when defined using a strict-tolerant standard ($\mathbf{st}$). Conversely, they proved that under a…

Goedel's completeness theorem is concerned with provability, while Girard's theorem in ludics (as well as full completeness theorems in game semantics) are concerned with proofs. Our purpose is to look for a connection between these two…

This paper concerns an expansion of first-order Belnap-Dunn logic whose connectives and quantifiers all have a counterpart in classical logic. The language and logical consequence relation of this paradefinite logic are defined, a sequent…

Partition logics -- non-Boolean event structures obtained by pasting Boolean algebras -- provide a natural language for situations in which a system has a definite latent state but can be accessed and resolved only through mutually…

Non-classical generalizations of classical modal logic have been developed in the contexts of constructive mathematics and natural language semantics. In this paper, we discuss a general approach to the semantics of non-classical modal…

The article explores the arithmetic of multiplication as a model of many valued projective logic. It is demonstrated that closed numerical intervals within this framework constitute Heyting algebras. The conditions for these algebras to be…

We prove that there are continuum-many axiomatic extensions of the full Lambek calculus with exchange that have the deductive interpolation property. Further, we extend this result to both classical and intuitionistic linear logic as well…

The aim of the present paper is to show that the concept of intuitionistic logic based on a Heyting algebra can be generalized in such a way that it is formalized by means of a bounded poset. In this case it is not assumed that the poset is…

Lawvere showed that generalised metric spaces are categories enriched over $[0, \infty]$, the quantale of the positive extended reals. The statement of enrichment is a quantitative analogue of being a preorder. Towards seeking a logic for…

In this paper we explore the design of sequent calculi operating on graphs. For this purpose, we introduce a set of logical connectives allowing us to extend the correspondence between cographs and classical propositional formulas to any…

Double-negation translations are used to encode and decode classical proofs in intuitionistic logic. We show that, in the cut-free fragment, we can simplify the translations and introduce fewer negations. To achieve this, we consider the…

Pomset logic introduced by Retor\'e is an extension of linear logic with a self-dual noncommutative connective. The logic is defined by means of proof-nets, rather than a sequent calculus. Later a deep inference system BV was developed with…

We introduce a notion of Kripke model for classical logic for which we constructively prove soundness and cut-free completeness. We discuss the novelty of the notion and its potential applications.

Cirquent calculus is a novel proof theory permitting component-sharing between logical expressions. Using it, the predecessor article "Elementary-base cirquent calculus I: Parallel and choice connectives" built the sound and complete…

Most non-classical logics are subclassical, that is, every inference/theorem they validate is also valid classically. A notable exception is the three-valued propositional Logic of Ordinary Discourse (OL) proposed and extensively motivated…

Any intermediate propositional logic (i.e., a logic including intuitionistic logic and contained in classical logic) can be extended to a calculus with epsilon- and tau-operators and critical formulas. For classical logic, this results in…