Related papers: First-order logic in the Medvedev lattice
Dummett's logic LC is intuitionistic logic extended with Dummett's axiom: for every two statements the first implies the second or the second implies the first. We present a natural deduction and a Curry-Howard correspondence for…
First order formulas in a relational signature can be considered as operations on the relations of an underlying set, giving rise to multisorted algebras we call first order algebras. We present universal axioms so that an algebra satisfies…
When teaching an elementary logic course to students who have a general scientific background but have never been exposed to logic, we have to face the problem that the notions of deduction rule and of derivation are completely new to them,…
This paper studies the relationship between labelled and nested calculi for propositional intuitionistic logic, first-order intuitionistic logic with non-constant domains and first-order intuitionistic logic with constant domains. It is…
We investigate a class of first-order temporal-epistemic logics for reasoning about multi-agent systems. We encode typical properties of systems including perfect recall, synchronicity, no learning, and having a unique initial state in…
This paper studies a first-order expansion of a combination C+J of intuitionistic and classical propositional logic, which was studied by Humberstone (1979) and del Cerro and Herzig (1996), from a proof-theoretic viewpoint. While C+J has…
We consider an extension of first-order logic with a recursion operator that corresponds to allowing formulas to refer to themselves. We investigate the obtained language under two different systems of semantics, thereby obtaining two…
A new totally algebraic formalism based on general, abstract ladder operators has been proposed. This approach heavily grounds in the superoperator formalism of Primas. However it is necessary to introduce many improvements in his…
We present a multi-modal action logic with first-order modalities, which contain terms which can be unified with the terms inside the subsequent formulas and which can be quantified. This makes it possible to handle simultaneously time and…
The construction of first-order logic and set theory gives rise to apparent circularities of mutual dependence, making it unclear which can act as a self-contained starting point in the foundation of mathematics. In this paper, we carry out…
A quantitative model of concurrent interaction is introduced. The basic objects are linear combinations of partial order relations, acted upon by a group of permutations that represents potential non-determinism in synchronisation. This…
We extend description logics (DLs) with non-monotonic reasoning features. We start by investigating a notion of defeasible subsumption in the spirit of defeasible conditionals as studied by Kraus, Lehmann and Magidor in the propositional…
Non-classical generalizations of classical modal logic have been developed in the contexts of constructive mathematics and natural language semantics. In this paper, we discuss a general approach to the semantics of non-classical modal…
We show that in quantum logic of closed subspaces of Hilbert space one cannot substitute quantum operations for classical (standard Hilbert space) ones and treat them as primitive operations. We consider two possible ways of such a…
We develop an algebraic notion of recognizability for languages of words indexed by countable linear orderings. We prove that this notion is effectively equivalent to definability in monadic second-order (MSO) logic. We also provide three…
Reasoning with quantifier expressions in natural language combines logical and arithmetical features, transcending strict divides between qualitative and quantitative. Our topic is this cooperation of styles as it occurs in common…
We continue our investigation into hybrid polyadic multi-sorted logic with a focus on expresivity related to the operational and axiomatic semantics of rogramming languages, and relations with first-order logic. We identify a fragment of…
G{\"o}del's completeness theorem for classical first-order logic is one of the most basic theorems of logic. Central to any foundational course in logic, it connects the notion of valid formula to the notion of provable formula.We survey a…
This paper presents categorical formulations of Turing, Medvedev, Muchnik, and Weihrauch reducibilities in Computability Theory, utilizing Lawvere doctrines. While the first notions lend themselves to a smooth categorical presentation,…
From the viewpoint of provability, we compare some Gentzen-type hypersequent calculi for first-order infinite-valued {\L}ukasiewicz logic and for first-order rational Pavelka logic with each other and with H\'ajek's Hilbert-type calculi for…