计算机科学中的逻辑

In the setting of DynFO, dynamic programs update the stored result of a query whenever the underlying data changes. This update is expressed in terms of first-order logic. We introduce a strategy for constructing dynamic programs that…

For a regular cardinal $\kappa$, a formula of the modal $\mu$-calculus is $\kappa$-continuous in a variable x if, on every model, its interpretation as a unary function of x is monotone and preserves unions of $\kappa$-directed sets. We…

We construct a geometry of interaction (GoI: dynamic modeling of Gentzen-style cut elimination) for multiplicative-additive linear logic (MALL) by employing Bucciarelli-Ehrhard indexed linear logic MALL(I) to handle the additives. Our…

In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around the difficulty of finding induction axioms which are sufficient for proving a…

We study the relational graph models that constitute a natural subclass of relational models of lambda-calculus. We prove that among the lambda-theories induced by such models there exists a minimal one, and that the corresponding…

Pomset logic introduced by Retor\'e is an extension of linear logic with a self-dual noncommutative connective. The logic is defined by means of proof-nets, rather than a sequent calculus. Later a deep inference system BV was developed with…

In the semantics of programming languages one can view programs as state transformers, or as predicate transformers. Recently the author has introduced state-and-effect triangles which capture this situation categorically, involving an…

In programming models with a reversible semantics, computational steps can be undone. This paper addresses the integration of reversible semantics into process languages for communication-centric systems equipped with behavioral types. In…

We propose a way of reasoning about minimal and maximal values of the weights of transitions in a weighted transition system (WTS). This perspective induces a notion of bisimulation that is coarser than the classic bisimulation: it relates…

In our implementation of geometric resolution, the most costly operation is subsumption testing (or matching): One has to decide for a three-valued, geometric formula, if this formula is false in a given interpretation. The formula contains…

The parameterized model-checking problem for a class of first-order sentences (queries) asks to decide whether a given sentence from the class holds true in a given relational structure (database); the parameter is the length of the…

The key to the proof-theoretic study of a logic is a proof calculus with a subformula property. Many different proof formalisms have been introduced (e.g. sequent, nested sequent, labelled sequent formalisms) in order to provide such…

This paper contributes to the techniques of topo-algebraic recognition for languages beyond the regular setting as they relate to logic on words. In particular, we provide a general construction on recognisers corresponding to adding one…

In this paper we study possibilities of interpolation and symbol elimination in extensions of a theory $\mathcal{T}_0$ with additional function symbols whose properties are axiomatised using a set of clauses. We analyze situations in which…

We consider the problem of deciding the satisfiability of quantifier-free formulas in the theory of finite sets with cardinality constraints. Sets are a common high-level data structure used in programming; thus, such a theory is useful for…

Models of complex systems are widely used in the physical and social sciences, and the concept of layering, typically building upon graph-theoretic structure, is a common feature. We describe an intuitionistic substructural logic called…

Clause-elimination procedures that simplify formulas in conjunctive normal form play an important role in modern SAT solving. Before or during the actual solving process, such procedures identify and remove clauses that are irrelevant to…

We investigate the extension of Monadic Second Order logic, interpreted over infinite words and trees, with generalized "for almost all" quantifiers interpreted using the notions of Baire category and Lebesgue measure.

Convolution is a ubiquitous operation in mathematics and computing. The Kripke semantics for substructural and interval logics motivates its study for quantale-valued functions relative to ternary relations. The resulting notion of…

In this paper we propose a complete axiomatization of the bisimilarity distance of Desharnais et al. for the class of finite labelled Markov chains. Our axiomatization is given in the style of a quantitative extension of equational logic…