Related papers: A sequent calculus with procedure calls

Following the idea of Subexponential Linear Logic and Stratified Bounded Linear Logic, we propose a new parameterized version of Linear Logic which subsumes other systems like ELL, LLL or SLL, by including variants of the exponential rules.…

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…

Linear temporal logic (LTL) is a specification language for finite sequences (called traces) widely used in program verification, motion planning in robotics, process mining, and many other areas. We consider the problem of learning LTL…

Calculi with control operators have been studied to reason about control in programming languages and to interpret the computational content of classical proofs. To make these calculi into a real programming language, one should also…

We introduce a functional calculus with simple syntax and operational semantics in which the calculi introduced so far in the Curry-Howard correspondence for Classical Logic can be faithfully encoded. Our calculus enjoys confluence without…

This paper employs the linear nested sequent framework to design a new cut-free calculus LNIF for intuitionistic fuzzy logic--the first-order G\"odel logic characterized by linear relational frames with constant domains. Linear nested…

Extending and generalizing the approach of 2-sequents (Masini, 1992), we present sequent calculi for the classical modal logics in the K, D, T, S4 spectrum. The systems are presented in a uniform way-different logics are obtained by tuning…

This paper shows connections between command injection attacks, continuations, and the Lambek calculus: certain command injections, such as the tautology attack on SQL, are shown to be a form of control effect that can be typed using the…

In this paper we investigate the question: 'How can A Foundational Classical Singlesuccedent Sequent Calculus be formulated?' The choice of this particular area of proof-theoretic study is based on a particular ground that is, to formulate…

This paper concerns the explicit treatment of substitutions in the lambda calculus. One of its contributions is the simplification and rationalization of the suspension calculus that embodies such a treatment. The earlier version of this…

We prove a symbolic calculus for a class of pseudodifferential operators, and discuss its applications to $L^2$-compactness via a compact version of the $T(1)$ theorem.

Recursive algebraic data types (term algebras, ADTs) are one of the most well-studied theories in logic, and find application in contexts including functional programming, modelling languages, proof assistants, and verification. At this…

We introduce a simple functional language foetus (lambda calculus with tuples, constructors and pattern matching) supplied with a termination checker. This checker tries to find a well-founded structural order on the parameters on the given…

We propose to use Tarski's least fixpoint theorem as a basis to define recursive functions in the calculus of inductive constructions. This widens the class of functions that can be modeled in type-theory based theorem proving tool to…

In "Cut Elimination for Gentzen's Sequent Calculus with Equality and Logic of Partial Terms" LNCS 7750,161-172(2013), we have shown that the cut rule is eliminable in two ground equational sequent calculi, to be denoted by EQ_M and EQ'. In…

Chain-of-Thought (CoT) is a critical technique in enhancing the reasoning ability of Large Language Models (LLMs), and latent reasoning methods have been proposed to accelerate the inefficient token-level reasoning chain. We notice that…

Linear-constraint loops are programs whose transition relation is specified by a system of linear inequalities. The termination problem asks, given a loop, whether it admits an infinite computation. Decidability of termination remains open…

In the present paper, we introduce a multi-type calculus for the logic of measurable Kleene algebras, for which we prove soundness, completeness, conservativity, cut elimination and subformula property. Our proposal imports ideas and…

We present an extension of the Temporal Logic Synthesis Format (TLSF). TLSF builds on standard LTL, but additionally supports high-level constructs, such as sets and functions, as well as parameters that allow a specification to define a…

Fractional calculus is the calculus of differentiation and integration of non-integer orders. In a recently paper (Annals of Physics 323 (2008) 2756-2778), the Fundamental Theorem of Fractional Calculus is highlighted. Based on this…