相关论文: On the Proof Complexity of Deep Inference

Scientific claims gain credibility by replicability, especially if replication under different circumstances and varying designs yields equivalent results. Aggregating results over multiple studies is, however, not straightforward, and when…

Proof-theoretic methods are developed for subsystems of Johansson's logic obtained by extending the positive fragment of intuitionistic logic with weak negations. These methods are exploited to establish properties of the logical systems.…

We incorporate strong negation in the theory of computable functionals TCF, a common extension of Plotkin's PCF and G\"{o}del's system $\mathbf{T}$, by defining simultaneously strong negation $A^{\mathbf{N}}$ of a formula $A$ and strong…

Cook and Reckhow 1979 pointed out that NP is not closed under complementation iff there is no propositional proof system that admits polynomial size proofs of all tautologies. Theory of proof complexity generators aims at constructing sets…

We draw connections between the various conjectures which are included in G. R\'emond's generalized Lehmer problems. Specifically, we show that the degree one form of his conjecture for the multiplicative group is, in a sense, almost as…

We prove that persuasion is an NP-complete problem.

Proofs in propositional logic are typically presented as trees of derived formulas or, alternatively, as directed acyclic graphs of derived formulas. This distinction between tree-like vs. dag-like structure is particularly relevant when…

The Dempster-Shafer theory has been extended recently for its application to expert systems. However, implementing the extended D-S reasoning model in rule-based systems greatly complicates the task of generating informative explanations.…

A folk theorem says higher order arithmetic has the proof theoretic strength of set theory with limited power set. This paper makes the theorem precise in terms of several axiom system based on ZF.

A major open problem in proof complexity is to demonstrate that random 3-CNFs with a linear number of clauses require super-polynomial size refutations in bounded-depth Frege systems. We take the first step towards addressing this question…

This paper discusses limitations of reflexive and diagonal arguments as methods of proof of limitative theorems (e.g. G\"odel's theorem on Entscheidungsproblem, Turing's halting problem or Chaitin-G\"odel's theorem). The fact, that a formal…

We show that constant-depth Frege systems with counting axioms modulo $m$ polynomially simulate Nullstellensatz refutations modulo $m$. Central to this is a new definition of reducibility from formulas to systems of polynomials with the…

Polynomial inequalities lie at the heart of many mathematical disciplines. In this paper, we consider the fundamental computational task of automatically searching for proofs of polynomial inequalities. We adopt the framework of…

One of the big challenges in the development of probabilistic relational (or probabilistic logical) modeling and learning frameworks is the design of inference techniques that operate on the level of the abstract model representation…

In this paper we develop cyclic proof systems for the problem of inclusion between the least sets of models of mutually recursive predicates, when the ground constraints in the inductive definitions belong to the quantifier-free fragments…

An inductive logic can be formulated in which the elements are not propositions or probability distributions, but information systems. The logic is complete for information systems with binary hypotheses, i.e., it applies to all such…

Statisticians are largely focused on developing methods that perform well in a frequentist sense -- even the Bayesians. But the widely-publicized replication crisis suggests that these performance guarantees alone are not enough to instill…

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, now several type systems based on circular reasoning have…

In this note we demonstrate that a number of case-heavy combinatorial proofs in the mathematical phylogenetics literature can be proven more compactly using computational support. We use these techniques to also prove several new…

In this paper we introduce a system AID (Alogtime Inductive Definitions) of bounded arithmetic. The main feature of AID is to allow a form of inductive definitions, which was extracted from Buss' propositional consistency proof of Frege…