Related papers: A joint logic of problems and propositions
After surveying classical results, we introduce a generalized notion of inference system to support structural recursion on non-well-founded data types. Besides axioms and inference rules with the usual meaning, a generalized inference…
A decade ago, Isham and Butterfield proposed a topos-theoretic approach to quantum mechanics, which meanwhile has been extended by Doering and Isham so as to provide a new mathematical foundation for all of physics. Last year, three of the…
We present a unified categorical treatment of completeness theorems for several classical and intuitionistic infinitary logics with a proposed axiomatization. This provides new completeness theorems and subsumes previous ones by G\"odel,…
In this article, we add a diamond to the parametrized box-based propositional language of intuitionistic doxastic logic and intuitionistic epistemic logic introduced by Artemov and Protopopescu. The main results of this article are the…
The present article is a brief informal survey of computability logic --- the game-semantically conceived formal theory of computational resources and tasks. This relatively young nonclassical logic is a conservative extension of classical…
Coalition logic is one of the most popular logics for multi-agent systems. While epistemic extensions of coalition logic have received much attention, existence of their complete axiomatisations has so far been an open problem. In this…
Our understanding about things is conceptual. By stating that we reason about objects, it is in fact not the objects but concepts referring to them that we manipulate. Now, so long just as we acknowledge infinitely extending notions such as…
Expectation is a central notion in probability theory. The notion of expectation also makes sense for other notions of uncertainty. We introduce a propositional logic for reasoning about expectation, where the semantics depends on the…
This article presents iALC, an intuitionistic version of the classical description logic ALC, based on the framework for constructive modal logics presented by Simpson \cite{simpson95} and related to description languages, via hybrid…
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…
Prawitz conjectured that the proof-theoretically valid logic is intuitionistic logic. Recent work on proof-theoretic validity has disproven this. In fact, it has been shown that proof-theoretic validity is not even closed under…
In this paper we study a model of intuitionistic higher-order logic which we call \emph{the Muchnik topos}. The Muchnik topos may be defined briefly as the category of sheaves of sets over the topological space consisting of the Turing…
In [17], we introduced a modal logic, called $L$, which combines intuitionistic propositional logic $IPC$ and classical propositional logic $CPC$ and is complete w.r.t. an algebraic semantics. However, $L$ seems to be too weak for…
We present a first-order probabilistic epistemic logic, which allows combining operators of knowledge and probability within a group of possibly infinitely many agents. The proposed framework is the first order extension of the logic of…
We analyse and develop the recent suggestion that a temporal form of quantum logic provides the natural mathematical framework within which to discuss the proposal by Gell-Mann and Hartle for a generalised form of quantum theory based on…
We have proposed in several recent papers a critical view of some parts of quantum mechanics (QM) that is methodologically unusual because it rests on analysing the language of QM by using some elementary but fundamental tools of…
An origin is often an intriguing issue. It becomes doubly intriguing when the logical form of thinking is considered. In this paper we will investigate exactly that: we will conjecture on the origin of basic instruments of logical thinking.…
Linear Logic refines Intuitionnistic Logic by taking into account the resources used during the proof and program computation. In the past decades, it has been extended to various frameworks. The most famous are indexed linear logics which…
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 foundations of quantum mechanics have been plagued by controversy throughout the 85 year history of the field. It is argued that lack of clarity in the formulation of basic philosophical questions leads to unnecessary obscurity and…