Related papers: Un \'enonc\'e et un texte inaugural
Underlying the theory of inferences, a primary task of logic is language analysis. Such a task can be understood as depending on a general theory of representation, taking as a starting point the idea that some entities (`` representations…
This is a largely expository paper about how groups arise or are of interest in model theory. Included are the following topics: classifying groups definable in specific structures or theories and the relation to algebraic groups, groups…
Incomputability as a mathematical notion arose from work of Alan Turing and Alonzo Church in the 1930s. Like Turing himself, it attracted less attention than it deserved beyond the confines of mathematics. Today our experiences in computer…
The paper attempts to convince that the orthodox interpretation of quantum mechanics does not contradict philosophical realism by throwing light onto certain properties of quantum systems that seem to have escaped attention as yet. The…
We introduce the notion of an approximation system as a generalization of Taylor approximation, and we give some first examples. Next we develop the general theory, including error bounds and a sufficient criterion for convergence. More…
In this preliminary note, we will illustrate our ideas on automated mechanisms for termination and non-termination reasoning.
Python's typing system has evolved pragmatically into a powerful but theoretically fragmented system, with scattered specifications. This paper proposes a formalization to address this fragmentation. The central contribution is a formal…
This paper is about the flow of inference between communicative intentions, discourse structure and the domain during discourse processing. We augment a theory of discourse interpretation with a theory of distinct mental attitudes and…
If we define classical foundational concepts constructively, and introduce non-algorithmic effective methods into classical mathematics, then we can bridge the chasm between truth and provability, and define computational methods that are…
So far, following the works of A.M. Turing, the algorithms were considered as the mathematical abstraction from which we could write programs for computers whose principle was based on the theoretical concept of Turing machine. We start…
This is the text of my habilitation thesis defended at the \'Ecole Normale Sup\'erieure. The topological string presents an arena in which many features of string theory proper, such as the interplay between worldsheet and target space…
Turing progressions have been often used to measure the proof-theoretic strength of mathematical theories. Turing progressions based on $n$-provability give rise to a $\Pi_{n+1}$ proof-theoretic ordinal. As such, to each theory $U$ we can…
In arXiv:1604.08705 the authors introduced the propositional modal logic $\textbf{TSC}$ (which stands for Turing Schmerl Calculus) which adequately describes the provable interrelations between different kinds of Turing progressions. The…
This paper gives a concise introduction into the basic theory of {\omega}-automata (as of March 2014). The starting point are the different types of recurrence conditions, modes of operation (deterministic, nondeterministic, alternating…
In this paper, we have compared r.e. sets based on their enumeration orders with Turing machines. Accordingly, we have defined novel concept uniformity for Turing machines and r.e. sets and have studied some relationships between uniformity…
Optics, aka functional references, are classes of tools that allow composable access into compound data structures. Usually defined as programming language libraries, they provide combinators to manipulate different shapes of data such as…
We define a generalization of the Turing machine that computes on general sets. Our main theorem states that the class of generalized Turing machine computable functions and the class of Set Recursive functions coincide.
We present a method to prove the decidability of provability in several well-known inference systems. This method generalizes both cut-elimination and the construction of an automaton recognizing the provable propositions.
Experimental research publications provide figure form resources including graphs, charts, and any type of images to effectively support and convey methods and results. To describe figures, authors add captions, which are often incomplete,…
This small overview of the General Theory is the kind of summary I would have liked to have read, before embarking in a comprehensive study of the General Theory at the time I was a student. As shown here, the main ideas are quite simple…