Related papers: Towards an Analysis of Proofs in Arithmetic

Proof nets are a syntax for linear logic proofs which gives a coarser notion of proof equivalence with respect to syntactic equality together with an intuitive geometrical representation of proofs. In this paper we give an alternative…

In this work, we explore proof theoretical connections between sequent, nested and labelled calculi. In particular, we show a general algorithm for transforming a class of nested systems into sequent calculus systems, passing through linear…

The key to the proof-theoretic study of a logic is a proof calculus with a subformula property. Many different proof formalisms have been introduced (e.g. sequent, nested sequent, labelled sequent formalisms) in order to provide such…

Formal deductive systems are very common in computer science. They are used to represent logics, programming languages, and security systems. Moreover, writing programs that manipulate them and that reason about them is important and…

We present a prototype of an integrated reasoning environment for educational purposes. The presented tool is a fragment of a proof assistant and automated theorem prover. We describe the existing and planned functionality of the theorem…

We present a form of algebraic reasoning for computational objects which are expressed as graphs. Edges describe the flow of data between primitive operations which are represented by vertices. These graphs have an interface made of…

We establish primitive recursive versions of some known facts about computable ordered fields of reals and computable reals, and then apply them to proving primitive recursiveness of some natural problems in linear algebra and analysis. In…

Commutativity has proven to be a powerful tool in reasoning about concurrent programs. Recent work has shown that a commutativity-based reduction of a program may admit simpler proofs than the program itself. The framework of…

Computational simulations are a popular method for testing hypotheses about the emergence of communication. This kind of research is performed in a variety of traditions including language evolution, developmental psychology, cognitive…

In this position paper, we propose a reasoning framework that can model the reasoning process underlying natural language inferences. The framework is based on the semantic tableau method, a well-studied proof system in formal logic. Like…

Almost from the inception of Hilbert's program, foundational and structural efforts in proof theory have been directed towards the goal of clarifying the computational content of modern mathematical methods. This essay surveys various…

Basic proof-search tactics in logic and type theory can be seen as the root-first applications of rules in an appropriate sequent calculus, preferably without the redundancies generated by permutation of rules. This paper addresses the…

Interactive proof assistants make it possible for ordinary mathematicians to write definitions and theorems in a formal proof language, like a programming language, so that a computer can parse them and check them against the rules of a…

Since the early twentieth century, it has been understood that mathematical definitions and proofs can be represented in formal systems systems with precise grammars and rules of use. Building on such foundations, computational proof…

We introduce proof terms for string rewrite systems and, using these, show that various notions of equivalence on reductions known from the literature can be viewed as different perspectives on the notion of causal equivalence. In…

Mathematical proofs are both paradigms of certainty and some of the most explicitly-justified arguments that we have in the cultural record. Their very explicitness, however, leads to a paradox, because the probability of error grows…

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 the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…

The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…

We present a comprehensive programme analysing the decomposition of proof systems for non-classical logics into proof systems for other logics, especially classical logic, using an algebra of constraints. That is, one recovers a proof…