相关论文: Cirquent calculus deepened
Inference systems are a widespread framework used to define possibly recursive predicates by means of inference rules. They allow both inductive and coinductive interpretations that are fairly well-studied. In this paper, we consider a…
Justification logics are modal-like logics that provide a framework for reasoning about justifications. This paper introduces labeled sequent calculi for justification logics, as well as for hybrid modal-justification logics. Using the…
Substitutions play a crucial role in a wide range of contexts, from analyzing the dynamics of social opinions and conducting mathematical computations to engaging in game-theoretical analysis. For many situations, considering one-step…
Debates concerning philosophical grounds for the validity of classical and intuitionistic logics often have the very nature of logical proofs as one of the main points of controversy. The intuitionist advocates for a strict notion of…
A cyclic proof system allows us to perform inductive reasoning without explicit inductions. We propose a cyclic proof system for HFLN, which is a higher-order predicate logic with natural numbers and alternating fixed-points. Ours is the…
Real-life conjectures do not come with instructions saying whether they they should be proven or, instead, refuted. Yet, as we now know, in either case the final argument produced had better be not just convincing but actually verifiable in…
We give a mathematical framework to describe the evolution of an open quantum systems subjected to finitely many interactions with classical apparatuses. The systems in question may be composed of distinct, spatially separated subsystems…
A logic is presented for reasoning on iterated sequences of formulae over some given base language. The considered sequences, or "schemata", are defined inductively, on some algebraic structure (for instance the natural numbers, the lists,…
This article has one single purpose: introduce a new and simple, yet highly insightful approach to capture, fully and quantitatively, the dynamics of the circular flow of income in economies. The proposed approach relies mostly on basic…
Our primary purpose is to isolate the abstract, mathematical properties of circuits -- both classical Boolean circuits and quantum circuits -- that are essential for their computational interpretation. A secondary purpose is to clarify the…
Logical paradoxes and inconsistent information pose deep challenges in epistemology and the philosophy of logic. Classical systems typically handle contradictions only through external checks or by altering the logical framework, as in…
The key to the proof-theoretic study of a logic is a proof calculus with a subformula property. Many different proof formalisms have been introduced (e.g. sequent, nested sequent, labelled sequent formalisms) in order to provide such…
This paper defines a new proof- and category-theoretic framework for classical linear logic that separates reasoning into one linear regime and two persistent regimes corresponding to ! and ?. The resulting linear/producer/consumer (LPC)…
We consider modal logic extended with the well-known temporal operator 'eventually' and provide a cut-elimination procedure for a cyclic sequent calculus that captures this fragment. The work showcases an adaptation of the reductive…
Uniform proofs are sequent calculus proofs with the following characteristic: the last step in the derivation of a complex formula at any stage in the proof is always the introduction of the top-level logical symbol of that formula. We…
In traditional justification logic, evidence terms have the syntactic form of polynomials, but they are not equipped with the corresponding algebraic structure. We present a novel semantic approach to justification logic that models…
We explore the theory of illfounded and cyclic proofs for the propositional modal $\mu$-calculus. A fine analysis of provability for classical and intuitionistic modal logic provides a novel bridge between finitary, cyclic and illfounded…
The purpose of this paper is to develop and study recursive proofs of coinductive predicates. Such recursive proofs allow one to discover proof goals in the construction of a proof of a coinductive predicate, while still allowing the use of…
In this paper, we establish the foundations of a novel logical framework for the {\pi}-calculus, based on the deduction-as-computation paradigm. Following the standard proof-theoretic interpretation of logic programming, we represent…
The recapture relationship is an important element to any understanding of the connexion between different systems of logic. Loosely speaking, one system of logic recaptures another if it is possible to specify a subsystem of the former…