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Developing suitable formal semantics can be of great help in the understanding, design and implementation of a programming language, and act as a guide for software development tools like analyzers or partial evaluators. In this sense, full…
We study Two-Variable First-Order Logic, FO2, under semantic constraints that model hierarchically structured data. Our first logic extends FO2 with a linear order < and a chain of increasingly coarser equivalence relations E_1, E_2, ... .…
We study on which classes of graphs first-order logic (FO) and monadic second-order logic (MSO) have the same expressive power. We show that for all classes C of graphs that are closed under taking subgraphs, FO and MSO have the same…
The stable model semantics had been recently generalized to non-Herbrand structures by several works, which provides a unified framework and solid logical foundations for answer set programming. This paper focuses on the expressiveness of…
This article presents a relatively complete proof calculus for the dynamic logic of communicating hybrid programs dLCHP. Beyond hybrid systems, communicating hybrid programs not only feature mixed discrete and continuous dynamics but also…
Hyperproperties are properties of systems that relate different executions traces, with many applications from security to symmetry, consistency models of concurrency, etc. In recent years, different linear-time logics for specifying…
It is well-known that every first-order property on words is expressible using at most three variables. The subclass of properties expressible with only two variables is also quite interesting and well-studied. We prove precise structure…
We introduce a generalized logic programming paradigm where programs, consisting of facts and rules with the usual syntax, can be enriched by co-facts, which syntactically resemble facts but have a special meaning. As in coinductive logic…
Modal logic is a paradigm for several useful and applicable formal systems in computer science. It generally retains the low complexity of classical propositional logic, but notable exceptions exist in the domains of description, temporal,…
One way to interpret the reasoning power of transformer-based language models is to describe the types of logical rules they can resolve over some input text. Recently, Chiang et al. (2023) showed that finite-precision transformers can be…
Once one has enriched LFG's formal machinery with the linear logic mechanisms needed for semantic interpretation as proposed by Dalrymple et. al., it is natural to ask whether these make any existing components of LFG redundant. As…
Multiple logic-based reconstructions of conceptual data modelling languages such as EER, UML Class Diagrams, and ORM exist. They mainly cover various fragments of the languages and none are formalised such that the logic applies…
There has recently been an increasing interest in declarative data analysis, where analytic tasks are specified using a logical language, and their implementation and optimisation are delegated to a general-purpose query engine. Existing…
Logic Programs with Ordered Disjunction (LPODs) extend classical logic programs with the capability of expressing preferential disjunctions in the heads of program rules. The initial semantics of LPODs, although simple and quite intuitive,…
We design various logics for proving hyper properties of iterative programs by application of abstract interpretation principles. In part I, we design a generic, structural, fixpoint abstract interpreter parameterized by an algebraic…
Spatial conjunction is a powerful construct for reasoning about dynamically allocated data structures, as well as concurrent, distributed and mobile computation. While researchers have identified many uses of spatial conjunction, its…
A Datalog program can be viewed as a syntactic specification of a functor from database instances over some schema to database instances over another schema. The same holds more generally for $\exists$Datalog. We establish large classes of…
Description logics are knowledge representation formalisms that provide the formal underpinning of the semantic web and in particular of the $\text{OWL}$ Ontology Web Language. In this paper we investigate the expressive power of logic…
We unify functional and logic programming by treating predicatesas functions equipped with their support: the set of inputs whose output is nonzero. Datalog, for instance, is a language of finitely supported boolean functions. Finite…
Order-invariant first-order logic is an extension of first-order logic FO where formulae can make use of a linear order on the structures, under the proviso that they are order-invariant, i.e. that their truth value is the same for all…