Related papers: Constructive Provability Logic
Intuitionistic logic extended with decidable propositional atoms combines classical properties in its propositional part and intuitionistic properties for derivable formulas not containing propositional symbols. Sequent calculus is used as…
This paper from 2012 is the second in a series of three papers. All three papers deal with interpretability logics and related matters. In the first paper a construction method was exposed to obtain models of these logics. Using this…
Defeasible logics provide several linguistic features to support the expression of defeasible knowledge. There is also a wide variety of such logics, expressing different intuitions about defeasible reasoning. However, the logics can only…
Nonmonotonic logics are usually characterized by the presence of some notion of 'conditional' that fails monotonicity. Research on nonmonotonic logics is therefore largely concerned with the defeasibility of argument forms and the…
We study various formulations of the completeness of first-order logic phrased in constructive type theory and mechanised in the Coq proof assistant. Specifically, we examine the completeness of variants of classical and intuitionistic…
Beloved Curry--Howard correspondence tells that types are intuitionistic propositions, and in constructive math, a proof of proposition can be seen as some kind of a construction, or witness, conveying the information of the proposition. We…
We develop a second-order extension of intuitionistic modal logic, allowing quantification over propositions, both syntactically and semantically. A key feature of second-order logic is its capacity to define positive connectives from the…
Pearl observes that causal knowledge enables predicting the effects of interventions, such as actions, whereas descriptive knowledge only permits drawing conclusions from observation. This paper extends Pearl's approach to causality and…
We present a propositional logic %which can be used to reason about the uncertainty of events, where the uncertainty is modeled by a set of probability measures assigning an interval of probability to each event. We give a sound and…
We derive an intuitionistic version of G\"odel-L\"ob modal logic ($\sf{GL}$) in the style of Simpson, via proof theoretic techniques. We recover a labelled system, $\sf{\ell IGL}$, by restricting a non-wellfounded labelled system for…
Argumentation is a promising model for reasoning with uncertain knowledge. The key concept of acceptability enables to differentiate arguments and counterarguments: The certainty of a proposition can then be evaluated through the most…
We find that second order quantification is problematic when a quantified concept variable is supposed to function predicatively. This issue is analyzed and it is shown that a constructive interpretation of the falling under relation…
The need for rigorous process composition is encountered in many situations pertaining to the development and analysis of complex systems. We discuss the use of Classical Linear Logic (CLL) for correct-by-construction resource-based process…
We carry out a semantic study of the constructive modal logic CK. We provide a categorical duality linking the algebraic and birelational semantics of the logic. We then use this to prove Sahlqvist style correspondence and completeness…
The logic of constant domains is intuitionistic logic extended with the so-called forall-shift axiom, a classically valid statement which implies the excluded middle over decidable formulas. Surprisingly, this logic is constructive and so…
This paper presents a novel explanation of the cause of quantum probabilities and the Born rule based on the intuitionistic interpretation of quantum mechanics where propositions obey constructive (intuitionistic) logic. The use of…
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…
Construction Grammar (CxG) has recently been used as the basis for probing studies that have investigated the performance of large pretrained language models (PLMs) with respect to the structure and meaning of constructions. In this…
Logic-based models can be used to build verification tools for machine learning classifiers employed in the legal field. ML classifiers predict the outcomes of new cases based on previous ones, thereby performing a form of case-based…
We propose a modular method for proving termination of general logic programs (i.e., logic programs with negation). It is based on the notion of acceptable programs, but it allows us to prove termination in a truly modular way. We consider…