27 citations · 49 across the 15 of their papers we have counts for
19 papers
Application of a generalization of Darbos fixed point theorem on an integral equation involving the weighted fractional integral with respect to another function
Sudip Deb, Anupam Das
In this study , we display a generalization of Darbos fixed point theorem , by using the use of a freshly made contraction operator and that we use to study the solvability of an i…
Cyclic proofs for arithmetical inductive definitions
Anupam Das, Lukas Melgaard
We investigate the cyclic proof theory of extensions of Peano Arithmetic by (finitely iterated) inductive definitions. Such theories are essential to proof theoretic analyses of ce…
Computational expressivity of (circular) proofs with fixed points
Gianluca Curzi, Anupam Das
We study the computational expressivity of proof systems with fixed point operators, within the 'proofs-as-programs' paradigm. We start with a calculus muLJ (due to Clairambault) t…
Non-uniform complexity via non-wellfounded proofs
Gianluca Curzi, Anupam Das
Cyclic and non-wellfounded proofs are now increasingly employed to establish metalogical results in a variety of settings, in particular for type systems with forms of (co)inductio…
Cyclic Proofs, Hypersequents, and Transitive Closure Logic
Anupam Das, Marianna Girlando
We propose a cut-free cyclic system for Transitive Closure Logic (TCL) based on a form of hypersequents, suitable for automated reasoning via proof search. We show that previously…
Enumerating Independent Linear Inferences
Anupam Das, Alex Rice
A linear inference is a valid inequality of Boolean algebra in which each variable occurs at most once on each side. In this work we leverage recently developed graphical represent…
Cyclic Implicit Complexity
Gianluca Curzi, Anupam Das
Circular (or cyclic) proofs have received increasing attention in recent years, and have been proposed as an alternative setting for studying (co)inductive reasoning. In particular…
Proof complexity of positive branching programs
Anupam Das, Avgerinos Delkos
We investigate the proof complexity of systems based on positive branching programs, i.e. non-deterministic branching programs (NBPs) where, for any 0-transition between two nodes,…
Beyond formulas-as-cographs: an extension of Boolean logic to arbitrary graphs
Cameron Calk, Anupam Das, Tim Waring
We propose a graph-based extension of Boolean logic called Boolean Graph Logic (BGL). Construing formula trees as the cotrees of cographs, we may state semantic notions such as eva…
Proof complexity of systems of (non-deterministic) decision trees and branching programs
Sam Buss, Anupam Das, Alexander Knop
This paper studies propositional proof systems in which lines are sequents of decision trees or branching programs - deterministic and nondeterministic. The systems LDT and LNDT ar…
From QBFs to MALL and back via focussing: fragments of multiplicative additive linear logic for each level of the polynomial hierarchy
Anupam Das
In this work we investigate how to extract alternating time bounds from 'focussed' proof systems. Our main result is the obtention of fragments of MALLw (MALL with weakening) compl…
A Functional (Monadic) Second-Order Theory of Infinite Trees
Anupam Das, Colin Riba
This paper presents a complete axiomatization of Monadic Second-Order Logic (MSO) over infinite trees. MSO on infinite trees is a rich system, and its decidability ("Rabin's Tree T…
On the logical complexity of cyclic arithmetic
Anupam Das
We study the logical complexity of proofs in cyclic arithmetic (), as introduced in Simpson '17, in terms of quantifier alternations of formulae occurring. Writing $CΣ…
Some Fibonacci sequence spaces of non-absolute type derived from with and Hausdorff measure of non-compactness of composition operators
Anupam Das, Bipan Hazarika, Feyzi Başar
The aim of the paper is to introduce the spaces and derived by the composition of the two infinite matrices an…
On linear rewriting systems for Boolean logic and some applications to proof theory
Anupam Das, Lutz Straßburger
Linear rules have played an increasing role in structural proof theory in recent years. It has been observed that the set of all sound linear inference rules in Boolean logic is al…
Some new Fibonacci difference spaces of non-absolute type and compact operators
Anupam Das, Bipan Hazarika
The aim of the paper is to introduced the spaces and which are the BK-spaces of non-absolute type and also derive some inclusion relations. Furthe…
Some properties of Generalized Fibonacci difference bounded and -absolutely convergent sequences
Anupam Das, Bipan Hazarika
The main objective of this paper is to introduced a new sequence space by using the band matrix We also establish a fe…
On Nested Sequents for Constructive Modal Logics
Lutz Strassburger, Anupam Das, Ryuta Arisaka
We present deductive systems for various modal logics that can be obtained from the constructive variant of the normal modal logic CK by adding combinations of the axioms d, t, b,…
On the relative proof complexity of deep inference via atomic flows
Anupam Das
We consider the proof complexity of the minimal complete fragment, KS, of standard deep inference systems for propositional logic. To examine the size of proofs we employ atomic fl…