Related papers: Proof Complexity of Substructural Logics

This paper shows how proof nets can be used to formalize the notion of ``incomplete dependency'' used in psycholinguistic theories of the unacceptability of center-embedded constructions. Such theories of human language processing can…

Several variants of linear logic have been proposed to characterize complexity classes in the proofs-as-programs correspondence. Light linear logic (LLL) ensures a polynomial bound on reduction time, and characterizes in this way polynomial…

We investigate the problem of safety verification of infinite-state parameterized programs that are formed based on a rich class of topologies. We introduce a new proof system, called parametric proof spaces, which exploits the underlying…

The generally accepted wisdom in computational circles is that pure proof verification is a solved problem and that the computationally hard elements and fertile areas of study lie in proof discovery. This wisdom presumably does hold for…

This article precisely defines huge proofs within the system of Natural Deduction for the Minimal implicational propositional logic \mil. This is what we call an unlimited family of super-polynomial proofs. We consider huge families of…

We study the derivational complexity of rewrite systems whose termination is provable in the dependency pair framework using the processors for reduction pairs, dependency graphs, or the subterm criterion. We show that the derivational…

It is well known that the resolution method (for propositional logic) is complete. However, completeness proofs found in the literature use an argument by contradiction showing that if a set of clauses is unsatisfiable, then it must have a…

Refinement transforms an abstract system model into a concrete, executable program, such that properties established for the abstract model carry over to the concrete implementation. Refinement has been used successfully in the development…

We develop an automated framework for proving lower bounds on the bilinear complexity of matrix multiplication over finite fields. Our approach systematically combines orbit classification of the restricted first matrix and dynamic…

In this work, we prove upper and lower bounds over fields of positive characteristics for several fragments of the Ideal Proof System (IPS), an algebraic proof system introduced by Grochow and Pitassi (J. ACM 2018). Our results extend the…

We pioneer a new technique that allows us to prove a multitude of previously open simulations in QBF proof complexity. In particular, we show that extended QBF Frege p-simulates clausal proof systems such as IR-Calculus, IRM-Calculus,…

This work is the first exploration of proof-theoretic semantics for a substructural logic. It focuses on the base-extension semantics (B-eS) for intuitionistic multiplicative linear logic (IMLL). The starting point is a review of…

In this work we study the cost of local and global proofs on distributed verification. In this setting the nodes of a distributed system are provided with a nondeterministic proof for the correctness of the state of the system, and the…

We introduce a non-wellfounded proof system for intuitionistic logic extended with inductive and co-inductive definitions, based on a syntax in which fixpoint formulas are annotated with explicit variables for ordinals. We explore the…

For current state-of-the-art DPLL SAT-solvers the two main bottlenecks are the amounts of time and memory used. In proof complexity, these resources correspond to the length and space of resolution proofs. There has been a long line of…

A fertile area of recent research has demonstrated concrete polynomial time lower bounds for solving natural hard problems on restricted computational models. Among these problems are Satisfiability, Vertex Cover, Hamilton Path, Mod6-SAT,…

Logic is the science of correct inferences and a logical system is a tool to prove assertions in a certain logic in a correct way. There are many logical systems, and many ways of formalizing them, e.g., using natural deduction or sequent…

In this paper we present tableau proof systems for various justification logics. We show that the tableau systems are sound and complete with respect to Mkrtychev models. In order to prove the completeness of the tableaux, we give a…

We prove the #P-hardness of the counting problems associated with various satisfiability, graph and combinatorial problems, when restricted to planar instances. These problems include \begin{romannum} \item[{}] {\sc 3Sat, 1-3Sat, 1-Ex3Sat,…

This paper discusses the semantics and proof theory of Nilsson's probabilistic logic, outlining both the benefits of its well-defined model theory and the drawbacks of its proof theory. Within Nilsson's semantic framework, we derive a set…