Related papers: Carnap's Early Metatheory: Scope and Limits
Possibility theory offers a framework where both Lehmann's "preferential inference" and the more productive (but less cautious) "rational closure inference" can be represented. However, there are situations where the second inference does…
Learning Analytics (LA) has rapidly expanded through practical and technological innovation, yet its foundational identity has remained theoretically under-specified. This paper addresses this gap by proposing the first axiomatic theory…
The Copenhagen interpretation of quantum mechanics, which first took shape in Bohr's landmark 1928 paper on complementarity, remains an enigma. Although many physicists are skeptical about the necessity of Bohr's philosophical conclusions,…
The capacitated arc routing problem (CARP) is a challenging combinatorial optimisation problem abstracted from many real-world applications, such as waste collection, road gritting and mail delivery. However, few studies considered dynamic…
The investigations on higher-order type theories and on the related notion of parametric polymorphism constitute the technical counterpart of the old foundational problem of the circularity (or impredicativity) of second and higher order…
We introduce the notion of limiting theories, giving examples and providing a sufficient condition under which the first order theory of a structure is the limit of the first order theories of a collection of substructures. We also give a…
Soon after he proposed three classic observational tests for the general theory of relativity, Einstein realised that a consistent description of the universe as a whole provided another important challenge for the theory. In this essay, we…
Claude Shannons information theory (1949) has had a revolutionary impact on communication science. A crucial property of his framework is that it decouples the meaning of a message from the mechanistic details from the actual communication…
In this paper, we present a preliminary work on an approach to fill the gap between logic-based argumentation and the numerous approaches to tackle the dynamics of abstract argumentation frameworks. Our idea is that, even when arguments and…
Charles Peirce develops a scheme for classifying different kinds of monadic, dyadic and triadic relations. His account of these different classes of relations figures prominently in the development of his algebraic and diagrammatic systems…
The information-theoretic point of view proposed by Leibniz in 1686 and developed by algorithmic information theory (AIT) suggests that mathematics and physics are not that different. This will be a first-person account of some doubts and…
Dependence logic, introduced in [8], cannot be axiomatized. However, first-order consequences of dependence logic sentences can be axiomatized, and this is what we shall do in this paper. We give an explicit axiomatization and prove the…
We prove that the problem of determining whether a finite logical matrix determines an algebraizable logic is complete for EXPTIME. The same result holds for the classes of order algebraizable, weakly algebraizable, equivalential and…
The optimal mass transportation was introduced by Monge some 200 years ago and is, today, the source of large number of results in analysis, geometry and convexity. Here I investigate a new, surprising link between optimal transformations…
Given a weakly compact cardinal $\kappa$, we give an axiomatization of intuitionistic first-order logic over $\mathcal{L}_{\kappa^+, \kappa}$ and prove it is sound and complete with respect to Kripke models. As a consequence we get the…
Building on previous work by Andr\'e Platzer, we present a formal language for Stochastic Differential Dynamic Logic, and define its semantics, axioms and inference rules. Compared to the previous effort, our account of the Stochastic…
Informally speaking, the categoricity of an axiom system means that its non-logical symbols have only one possible interpretation that renders the axioms true. Although non-categoricity has become ubiquitous in the second half of the 20th…
The persisting gap between the formal and the informal mathematics is due to an inadequate notion of mathematical theory behind the current formalization techniques. I mean the (informal) notion of axiomatic theory according to which a…
This paper addresses the actual practice of justifying definitions in mathematics. First, I introduce the main account of this issue, namely Lakatos's proof-generated definitions. Based on a case study of definitions of randomness in…
In 1932, G\"odel proved that there is no finite semantics for intuitionistic logic. We consider all fragments of intuitionistic logic and check in each case whether a finite semantics exists. We may fulfill a didactic goal, as little logic…