相关论文: Consistency, non triviality and redundancy in math…

We present two possible criteria quantifying the degree of classicality of an arbitrary (finite dimensional) dynamical system. The inputs for these criteria are the classical dynamical structure of the system together with the quantum and…

This paper outlines a general formal framework for reasoning systems, intended to support future analysis of inference architectures across domains. We model reasoning systems as structured tuples comprising phenomena, explanation space,…

This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…

A method for testing nonlinearity in time series is described based on information-theoretic functionals -- redundancies, linear and nonlinear forms of which allow either qualitative, or, after incorporating the surrogate data technique,…

This paper analyzes the working or default assumptions researchers in the formal, statistical, and case study traditions typically hold regarding the sources of unexplained variance, the meaning of outliers, parameter values, human…

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…

Results about the redundancy of circumscriptive and default theories are presented. In particular, the complexity of establishing whether a given theory is redundant is establihsed.

Inclusion of redundant fundamental quantities in SI system has resulted in lot of ambiguities and confusion in modern theories. The incompatibilities between the existing theories can possibly be due to incorrect assumption of fundamental…

Mathematical proofs are often said to justify their conclusions by indicating the existence of a corresponding formal derivation. We argue that this widespread view relies on an under-examined notion of correspondence, or what it means for…

We study properties related to relevance in non-monotonic consequence relations obtained by systems of structured argumentation. Relevance desiderata concern the robustness of a consequence relation under the addition of irrelevant…

Formal logic has often been seen as uniquely placed to analyze mathematical argumentation. While formal logic is certainly necessary for a complete understanding of mathematical practice, it is not sufficient. Important aspects of…

In this note I describe reliability standards for writing and reviewing mathematical papers; these standards are (in my opinion) vital for the progress of mathematics. I give examples of applying the described or other reliability…

Stability is among the most important concepts in dynamical systems. Local stability is well-studied, whereas determining how "globally stable" a nonlinear system is very challenging. Over the last few decades, many different ideas have…

Consistency properties of concurrent computations, e.g., sequential consistency, linearizability, or eventual consistency, are essential for devising correct concurrent algorithms. In this paper, we present a logical formalization of such…

A thorough investigation of the foundations of paraconsistent logics. Relations between logical principles are formally studied, a novel notion of consistency is introduced, the logics of formal inconsistency, and the subclasses of…

We report complexity results about redundancy of formulae in 2CNF form. We first consider the problem of checking redundancy and show some algorithms that are slightly better than the trivial one. We then analyze problems related to finding…

In his Discourse on the Method of Rightly Conducting the Reason, and Seeking Truth in the Sciences, Rene Descartes sought ``clear and certain knowledge of all that is useful in life.'' Almost three centuries later, in ``The foundations of…

The importance of transformations and normal forms in logic programming, and generally in computer science, is well documented. This paper investigates transformations and normal forms in the context of Defeasible Logic, a simple but…

We seek to find normative criteria of adequacy for nonmonotonic logic similar to the criterion of validity for deductive logic. Rather than stipulating that the conclusion of an inference be true in all models in which the premises are…

In this note we will show how to get consistency for first order classical logic, in a purely syntactic way, without going through cut elimination. The procedure is very simple and it uses the calculus of structures in an essential way. It…