Related papers: On the convergence of reduction-based and model-ba…

The reflection principle is the statement that if a sentence is provable then it is true. Reflection principles have been studied for first-order theories, but they also play an important role in propositional proof complexity. In this…

The normal forms of different one- and two- parametric solutions of Thirring model are connected with each other by making use of generalized conformal shift transformations. A new alternative sources of superselection rules are shown and…

The simulation of electric rotating machines is both computationally expensive and memory intensive. To overcome these costs, model order reduction techniques can be applied. The focus of this contribution is especially on machines that…

We generalize the notion of proof term to the realm of transfinite reduction. Proof terms represent reductions in the first-order term format, thereby facilitating their formal analysis. We show that any transfinite reduction can be…

We describe an algorithmic method of proof compression based on the introduction of Pi_2-cuts into a cut-free LK-proof. The current approach is based on an inversion of Gentzen s cut-elimination method and extends former methods for…

Geometric modeling by constraints leads to large systems of algebraic equations. This paper studies bipartite graphs underlaid by systems of equations. It shows how these graphs make possible to polynomially decompose these systems into…

We present a sequent calculus for the modal Grzegorczyk logic Grz allowing non-well-founded proofs and obtain the cut-elimination theorem for it by constructing a continuous cut-elimination mapping acting on these proofs.

In this paper we present a constructive proof of cut elimination for a system of full second order logic with the structural rules absorbed and using sets instead of sequences. The standard problem of the cutrank growth is avoided by using…

Model merging, typically on Instruct and Thinking models, has shown remarkable performance for efficient reasoning. In this paper, we systematically revisit the simplest merging method that interpolates two weights directly. Particularly,…

We examine some combinatorial properties of parallel cut elimination in multiplicative linear logic (MLL) proof nets. We show that, provided we impose a constraint on some paths, we can bound the size of all the nets satisfying this…

In various provers and deductive verification tools, logical transformations are used extensively in order to reduce a proof task into a number of simpler tasks. Logical transformations are often part of the trusted base of such tools. In…

We present a complete proof synthesis method for the eight type systems of Barendregt's cube extended with $\eta$-conversion. Because these systems verify the proofs-as-objects paradigm, the proof synthesis method is a one level process…

Coinduction refers to both a technique for the definition of infinite streams, so-called codata, and a technique for proving the equality of coinductively specified codata. This article first reviews coinduction in declarative programming.…

Within the program of finding axiomatizations for various parts of computability logic, it was proved earlier that the logic of interactive Turing reduction is exactly the implicative fragment of Heyting's intuitionistic calculus. That sort…

Based on an analysis of the inference rules used, we provide a characterization of the situations in which classical provability entails intuitionistic provability. We then examine the relationship of these derivability notions to uniform…

The Circularity Principle was successfully applied for developing a coinductive proving technique, known as circular coinduction. In this paper, we show that the same principle can be used to develop an inductive proving technique. A main…

We develop a model of abduction in abstract argumentation, where changes to an argumentation framework act as hypotheses to explain the support of an observation. We present dialogical proof theories for the main decision problems (i.e.,…

A cut-and-paste model which mimics a trial-and-error process of adaptation is introduced and solved. The model, which can be thought of as a diffusion process with memory, is characterized by two properties, efficiency and persistence. We…

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…

Deduction modulo is a way to express a theory using computation rules instead of axioms. We present in this paper an extension of deduction modulo, called Polarized deduction modulo, where some rules can only be used at positive…