Related papers: Fibred Coalgebraic Logic and Quantum Protocols
We extend the {\lambda}-calculus with constructs suitable for relational and functional-logic programming: non-deterministic choice, fresh variable introduction, and unification of expressions. In order to be able to unify…
Algebraic logic studies algebraic theories related to proposition and first-order logic. A new algebraic approach to first-order logic is sketched in this paper. We introduce the notion of a quantifier theory, which is a functor from the…
It is proposed the scheme of quantum mechanics, in which a Hilbert space and the linear operators are not primary elements of the theory. Instead of it certain variant of the algebraic approach is considered. The elements of noncommutative…
By using the abstract structures investigated in the first Part of this article, we develop a semantics for an epistemic language, which expresses sentences like "Alice knows that Bob does not understand that PI is irrational". One is…
We explore a simple approach to quantum logic based on hybrid and dynamic modal logic, where the set of states is given by some Hilbert space. In this setting, a notion of quantum clause is proposed in a similar way the notion of Horn…
This paper studies nested sequents for quantified modal logics. In particular, it considers extensions of the propositional modal logics definable by the axioms D, T, B, 4, and 5 with varying, increasing, decreasing, and constant domains.…
A modal logic is \emph{non-iterative} if it can be defined by axioms that do not nest modal operators, and \emph{rank-1} if additionally all propositional variables in axioms are in scope of a modal operator. It is known that every…
Reliable verification techniques for quantum communication protocols are of paramount importance, given their high implementation cost and critical contexts of application. Extensions of process calculi have been proposed, together with…
We advocate here the use of computational logic for systems biology, as a \emph{unified and safe} framework well suited for both modeling the dynamic behaviour of biological systems, expressing properties of them, and verifying these…
We provide a compositional coalgebraic semantics for strategic games. In our framework, like in the semantics of functional programming languages, coalgebras represent the observable behaviour of systems derived from the behaviour of the…
We conduct the first detailed analysis in quantum information of recently derived operator relations from the study of quantum one-way local operations and classical communications (LOCC). We show how operator structures such as operator…
As a cornerstone of automated reasoning, equational reasoning finds equivalences between symbolic expressions and fuels advances across scientific disciplines. Yet, its potential remains limited by the exponential growth of equivalent…
We study extensions of standard description logics to the framework of polyadic modal logic. We promote a natural approach to such logics via general relation algebras that can be used to define operations on relations of all arities. As a…
Computability logic is a formal theory of computational tasks and resources. Its formulas represent interactive computational problems, logical operators stand for operations on computational problems, and validity of a formula is…
We investigate the combination of fragments of classical logic as a way of conservatively extending a given Boolean logic by the addition of new connectives, and we precisely characterize the circumstances in which such a combination…
We study the finitary version of the coalgebraic logic introduced by L. Moss. The syntax of this logic, which is introduced uniformly with respect to a coalgebraic type functor, required to preserve weak pullbacks, extends that of classical…
Quantum information has suggested new forms of quantum logic, called quantum computational logics, where meanings of sentences are represented by pieces of quantum information (generally, density operators of some Hilbert spaces), which can…
Formal, mathematically rigorous programming language semantics are the essential prerequisite for the design of logics and calculi that permit automated reasoning about concurrent programs. We propose a novel modular semantics designed to…
We apply to logic programming some recently emerging ideas from the field of reduction-based communicating systems, with the aim of giving evidence of the hidden interactions and the coordination mechanisms that rule the operational…
This report introduces a novel class of reasoning architectures, termed Quantum Circuit Reasoning Models (QCRM), which extend the concept of Variational Quantum Circuits (VQC) from energy minimization and classification tasks to structured…