计算机科学中的逻辑

Up-to techniques' represent enhancements of the coinduction proof method and are widely used on coinductive behavioural relations such as bisimilarity. Abstract formulations of these coinductive techniques exist, using fixed-points or…

Reversible CCS (RCCS) is a well-established, formal model for reversible communicating systems, which has been built on top of the classical Calculus of Communicating Systems (CCS). In its original formulation, each CCS process is equipped…

We present a generalisation of the theory of quantitative algebras of Mardare, Panangaden and Plotkin where (i) the carriers of quantitative algebras are not restricted to be metric spaces and can be arbitrary fuzzy relations or generalised…

We analyse the power of graph neural networks (GNNs) in terms of Boolean circuit complexity and descriptive complexity. We prove that the graph queries that can be computed by a polynomial-size bounded-depth family of GNNs are exactly those…

We present an ongoing effort to implement Universal Algebra in the UniMath system. Our aim is to develop a general framework for formalizing and studying Universal Algebra in a proof assistant. By constituting a formal system for isolating…

In deductive verification and software model checking, dealing with certain specification language constructs can be problematic when the back-end solver is not sufficiently powerful or lacks the required theories. One way to deal with this…

Multiple-environment MDPs (MEMDPs) capture finite sets of MDPs that share the states but differ in the transition dynamics. These models form a proper subclass of partially observable MDPs (POMDPs). We consider the synthesis of policies…

Propositional dynamic logic (PDL) is an important modal logic used to specify and reason about the behavior of software. A challenging problem in the context of PDL is solving fixed-point equations, i.e., formulae of the form $x \equiv…

This article explores the concept of transferability within communication channels, with a particular focus on the inability to transmit certain situations through these channels. The Channel Non-Transferability Theorem establishes that no…

The paper discusses properties of a DATALOG$^{\neg\neg}$-like query language 4QL, originally outlined in [MS10]. Negated literals in heads of rules naturally lead to inconsistencies. On the other hand, rules do not have to attach meaning to…

We present a sequent calculus for first-order logic with lambda terms and definite descriptions. The theory formalised by this calculus is essentially Russellian, but avoids some of its well known drawbacks and treats definite description…

Satisfiability modulo theories (SMT) is a core tool in formal verification. While the SMT-LIB specification language can be used to interact with theorem proving software, a high-level interface allows for faster and easier specifications…

This tutorial gives an advanced introduction to string diagrams and graph languages for higher-order computation. The subject matter develops in a principled way, starting from the two dimensional syntax of key categorical concepts such as…

Properties such as provable security and correctness for randomized programs are naturally expressed relationally as approximate equivalences. As a result, a number of relational program logics have been developed to reason about such…

We further develop the algebraic approach to input/output logic initiated in \cite{wollic22}, where subordination algebras and a family of their generalizations were proposed as a semantic environment of various input/output logics. In…

We present a bisequent calculus (BSC) for the minimal theory of definite descriptions (DD) in the setting of neutral free logic, where formulae with non-denoting terms have no truth value. The treatment of quantifiers, atomic formulae and…

We present a uniform characterisation of three-valued logics by means of the bisequent calculus (BSC). It is a generalised form of a sequent calculus (SC) where rules operate on the ordered pairs of ordinary sequents. BSC may be treated as…

Finster and Mimram have defined a dependent type theory called CaTT, which describes the structure of omega-categories. Types in homotopy type theory with their higher identity types form weak omega-groupoids, so they are in particular weak…

We provide a version of first-order hybrid tense logic with predicate abstracts and definite descriptions as the only non-rigid terms. It is formalised by means of a tableau calculus working on sat-formulas. A particular theory of DD…

Whereas the semantics of probabilistic languages has been extensively studied, specification languages for their properties have received less attention -- with the notable exception of recent and on-going efforts by Joost-Pieter Katoen and…