计算机科学中的逻辑

Monadic Second-Order Logic (MSO) extends First-Order Logic (FO) with variables ranging over sets and quantifications over those variables. We introduce and study Monadic Tree Logic (MTL), a fragment of MSO interpreted on infinite-tree…

Cyber-physical systems (CPSes), such as autonomous vehicles, use sophisticated components like ML-based controllers. It is difficult to provide evidence about the safe functioning of such components. To overcome this problem, Runtime…

In this paper, we study the finite satisfiability problem for the logic BE under the homogeneity assumption. BE is the cornerstone of Halpern and Shoham's interval temporal logic, and features modal operators corresponding to the prefix…

We present a lattice of distributed program specifications, whose ordering represents implementability/refinement. Specifications are modelled by families of subsets of relative execution traces, which encode the local orderings of state…

This paper considers a formalisation of classical logic using general introduction rules and general elimination rules. It proposes a definition of `maximal formula', `segment' and `maximal segment' suitable to the system, and gives…

We introduce and study a learning theory which is roughly automatic, that is, it does not require but a minimum of initial programming, and is based on the potential computational phenomenon of self-reference, (i.e. the potential ability of…

This paper continues the discussion of the representation of ontologies in the first-order logical environment FOLE. According to Gruber, an ontology defines the primitives with which to model the knowledge resources for a community of…

We give a simple and direct proof that super-consistency implies the cut elimination property in deduction modulo. This proof can be seen as a simplification of the proof that super-consistency implies proof normalization. It also takes…

We introduce and develop a set-based semantics for asynchronous TeamLTL. We consider two canonical logics in this setting: the extensions of TeamLTL by the Boolean disjunction and by the Boolean negation. We establish fascinating…

This paper discusses the representation of ontologies in the first-order logical environment {\ttfamily FOLE}. An ontology defines the primitives with which to model the knowledge resources for a community of discourse. These primitives…

We present a Julia package, DisjunctiveProgramming.jl, that extends the functionality in JuMP.jl to allow modeling problems via logical propositions and disjunctive constraints. Such models can then be reformulated into Mixed-Integer…

Interactive Theorem Provers (ITPs) are an indispensable tool in the arsenal of formal method experts as a platform for construction and (formal) verification of proofs. The complexity of the proofs in conjunction with the level of expertise…

We discuss the theory of Lie algebras in Lean's Mathlib library. Using nilpotency as the theme, we outline a computer formalisation of Engel's theorem and an application to root space theory. We emphasise that all arguments work with…

We introduce CPDL+, a family of expressive logics rooted in Propositional Dynamic Logic (PDL). In terms of expressive power, CPDL+ strictly contains PDL extended with intersection and converse (a.k.a. ICPDL) as well as Conjunctive Queries…

We study the conservativity of extensions by additional strict equalities of dependent type theories (and more general second-order generalized algebraic theories). The conservativity of Extensional Type Theory over Intensional Type Theory…

In the mid 80s, Lichtenstein, Pnueli, and Zuck showed that every formula of Past LTL (the extension of Linear Temporal Logic with past operators) is equivalent to a conjunction of formulas of the form $\mathbf{G}\mathbf{F} \varphi \vee…

We consider the following problem: given $d \times d$ rational matrices $A_1, \ldots, A_k$ and a polyhedral cone $\mathcal{C} \subset \mathbb{R}^d$, decide whether there exists a non-zero vector whose orbit under multiplication by $A_1,…

The uniform one-dimensional fragment of first-order logic, U1, is a formalism that extends two-variable logic in a natural way to contexts with relations of all arities. We survey properties of U1 and investigate its relationship to…

Homology groups of labelled asynchronous transition systems and Petri nets are introduced. Examples of computing the homology groups are given. It is proved that if labelled asynchronous transition systems are bisimulation equivalent, then…

In many QBF encodings, sequences of Boolean variables stand for binary representations of integer variables. Examples are state labels in bounded model checking or actions in planning problems. Often not the full possible range is used,…