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Introduction

Additional affiliations

November 2019 - present

July 2017 - October 2019

January 2016 - June 2017

## Publications

Publications (51)

In this paper, we study a novel approach to asynchronous hyperproperties by reconsidering the foundations of temporal team semantics. We consider three logics: , and , which are obtained by adding quantification over so-called time evaluation functions controlling the asynchronous progress of traces. We then relate synchronous to our new logics and...

Probabilistic team semantics is a framework for logical analysis of probabilistic dependencies. Our focus is on the axiomatizability, complexity, and expressivity of probabilistic inclusion logic and its extensions. We identify a natural fragment of existential second-order logic with additive real arithmetic that captures exactly the expressivity...

In this paper, we study a novel approach to asynchronous hyperproperties by reconsidering the foundations of temporal team semantics. We consider three logics: TeamLTL, TeamCTL and TeamCTL*, which are obtained by adding quantification over so-called time evaluation functions controlling the asynchronous progress of traces. We then relate synchronou...

In this work we analyse the parameterised complexity of propositional inclusion (PINC) and independence logic (PIND). The problems of interest are model checking (MC) and satisfiability (SAT). The complexity of these problems is well understood in the classical (non-parameterised) setting. Mahmood and Meier (FoIKS 2020) recently studied the paramet...

Probabilistic team semantics is a framework for logical analysis of probabilistic dependencies. Our focus is on the complexity and expressivity of probabilistic inclusion logic and its extensions. We identify a natural fragment of existential second-order logic with additive real arithmetic that captures exactly the expressivity of probabilistic in...

We propose logical characterizations of problems solvable in deterministic polylogarithmic time (PolylogTime) and polylogarithmic space (PolylogSpace). We introduce a novel two-sorted logic that separates the elements of the input domain from the bit positions needed to address these elements. We prove that the inflationary and partial fixed point...

Probabilistic team semantics is a framework for logical analysis of probabilistic dependencies. Our focus is on the complexity and expressivity of probabilistic inclusion logic and its extensions. We identify a natural fragment of existential second-order logic with additive real arithmetic that captures exactly the expressivity of probabilistic in...

We study the expressivity and the model checking problem of linear temporal logic with team semantics (TeamLTL). In contrast to LTL, TeamLTL is capable of defining hyperproperties, i.e., properties which relate multiple execution traces. Logics for hyperproperties have so far been mostly obtained by extending temporal logics like LTL and QPTL with...

Team semantics is the mathematical framework of modern logics of dependence and independence in which formulae are interpreted by sets of assignments (teams) instead of single assignments as in first-order logic. In order to deepen the fruitful interplay between team semantics and database dependency theory, we define Polyteam Semantics in which fo...

Second-order Boolean logic is a generalization of QBF, whose constant alternation fragments are known to be complete for the levels of the exponential time hierarchy. We consider two types of restriction of this logic: 1) restrictions to term constructions, 2) restrictions to the form of the Boolean matrix. Of the first sort, we consider two kinds...

We introduce a novel variant of BSS machines called Separate Branching BSS machines (S-BSS in short) and develop a Fagin-type logical characterisation for languages decidable in non-deterministic polynomial time by S-BSS machines. We show that NP on S-BSS machines is strictly included in NP on BSS machines and that every NP language on S-BSS machin...

The class of fully generic queries on complex objects was introduced by Beeri, Milo and Ta-Shma in 1997. Such queries are still relevant as they capture the class of manipulations on nested big data, where output can be generated without a need for looking in detail at, or comparing, the atomic data elements. Unfortunately, the class of fully gener...

We propose a logical characterization of problems solvable in deterministic polylogarithmic time (\(\mathrm {PolylogTime}\)). We introduce a novel two-sorted logic that separates the elements of the input domain from the bit positions needed to address these elements. In the course of proving that our logic indeed captures \(\mathrm {PolylogTime}\)...

We study probabilistic team semantics which is a semantical framework allowing the study of logical and probabilistic dependencies simultaneously. We examine and classify the expressive power of logical formalisms arising by different probabilistic atoms such as conditional independence and different variants of marginal distribution equivalences....

We study model and frame definability of various modal logics. Let ML(u⃞+) denote the fragment of modal logic extended with the universal modality in which the universal modality occurs only positively. We show that a class of Kripke models is definable in ML(u⃞+) if and only if the class is elementary and closed under disjoint unions and surjectiv...

We propose a logical characterization of problems solvable in deterministic polylogarithmic time (PolylogTime). We introduce a novel, two-sorted logic that separates the elements of the input domain from the bit positions needed to address these elements. In the course of proving that our logic indeed captures PolylogTime on finite ordered structur...

We study probabilistic team semantics which is a semantical framework allowing the study of logical and probabilistic dependencies simultaneously. We examine and classify the expressive power of logical formalisms arising by different probabilistic atoms such as conditional independence and different variants of marginal distribution equivalences....

We define a variant of team semantics called multiteam semantics based on
multisets and study the properties of various logics in this framework. In
particular, we define natural probabilistic versions of inclusion and
independence atoms and certain approximation operators motivated by approximate
dependence atoms of V\"a\"an\"anen.

Team semantics is a semantical framework for the study of dependence and independence concepts ubiquitous in many areas such as databases and statistics. In recent works team semantics has been generalised to accommodate also multisets and probabilistic dependencies. In this article we study a variant of probabilistic team semantics and relate this...

Second-order transitive-closure logic, SO(TC), is an expressive declarative language that captures the complexity class PSPACE. Already its monadic fragment, MSO(TC), allows the expression of various NP-hard and even PSPACE-hard problems in a natural and elegant manner. As SO(TC) offers an attractive framework for expressing properties in terms of...

Team semantics is a semantical framework for the study of dependence and independence concepts ubiquitous in many areas such as databases and statistics. In recent works team semantics has been generalised to accommodate also multisets and probabilistic dependencies. In this article we study a variant of probabilistic team semantics and relate this...

We classify the computational complexity of the satisfiability, validity, and model-checking problems for propositional independence, inclusion, and team logic. Our main result shows that the satisfiability and validity problems for propositional team logic are complete for alternating exponential-time with polynomially many alternations.

Team semantics is the mathematical framework of modern logics of dependence and independence in which formulae are interpreted by sets of assignments (teams) instead of single assignments as in first-order logic. In order to deepen the fruitful interplay between team semantics and database dependency theory, we define Polyteam Semantics in which fo...

Team semantics is the mathematical framework of modern logics of dependence and independence in which formulae are interpreted by sets of assignments (teams) instead of single assignments as in first-order logic. In order to deepen the fruitful interplay between team semantics and database dependency theory, we define Polyteam Semantics in which fo...

Team semantics is the mathematical framework of modern logics of dependence and independence in which formulae are interpreted by sets of assignments (teams) instead of single assignments as in first-order logic. In order to deepen the fruitful interplay between team semantics and database dependency theory, we define "Polyteam Semantics" in which...

We introduce a new variant of dependence logic ( ) called Boolean dependence logic ( ). In dependence atoms are of the type , where α is a Boolean variable. Intuitively, with Boolean dependence atoms one can express quantification of relations, while standard dependence atoms express quantification over functions. We compare the expressive powers o...

Modal inclusion logic is a formalism that belongs to the family of logics based on team semantics. This article investigates the model checking and validity problems of propositional and modal inclusion logics. We identify complexity bounds for both problems, covering both lax and strict team semantics. Thereby we tie some loose ends related to the...

We study quantified propositional logics from the complexity theoretic point of view. First we introduce alternating dependency quantified boolean formulae (ADQBF) which generalize both quantified and dependency quantified boolean formulae. We show that the truth evaluation for ADQBF is AEXPTIME(poly)-complete. We also identify fragments for which...

Let
denote the fragment of modal logic extended with the universal modality in which the universal modality occurs only positively. We characterise the relative definability of
relative to finite transitive frames in the spirit of the well-known Goldblatt–Thomason theorem. We show that a class \(\mathbb {F}\) of finite transitive frames is definabl...

We study the complexity of the validity problems of propositional dependence logic, modal dependence logic, and extended modal dependence logic. We show that the validity problem for propositional dependence logic is -complete. In addition, we establish that the corresponding problems for modal dependence logic and extended modal dependence logic c...

Let ML(U^+) denote the fragment of modal logic extended with the universal modality in which the universal modality occurs only positively. We characterize the relative definability of ML(U^+) relative to finite transitive frames in the spirit of the well-known Goldblatt-Thomason theorem. We show that a class F of Kripke frames is definable in ML(U...

We define a variant of team semantics called multiteam semantics based on multisets and study the properties of various logics in this framework. In particular, we define natural probabilistic versions of inclusion and independence atoms and certain approximation operators motivated by approximate dependence atoms of Väänänen.

We introduce two variants of computation tree logic CTL based on team semantics: an asynchronous one and a synchronous one. For both variants we investigate the computational complexity of the satisfiability as well as the model checking problem. The satisfiability problem is shown to be EXPTIME-complete. Here it does not matter which of the two se...

We introduce two variants of computation tree logic CTL based on team semantics: an asynchronous one and a synchronous one. For both variants we investigate the computational complexity of the satisfiability as well as the model checking problem. The satisfiability problem is shown to be EXPTIME-complete. Here it does not matter which of the two se...

We classify the computational complexity of the satisfiability, validity and model-checking problems for propositional independence and inclusion logic and their extensions by the classical negation.

Let
denote the fragment of modal logic extended with the universal modality in which the universal modality occurs only positively. We characterize the definability of
in the spirit of the well-known Goldblatt–Thomason theorem. We show that an elementary class \({\mathbb {F}}\) of Kripke frames is definable in
if and only if \({\mathbb {F}}\) is cl...

This work presents a classification of weak models of distributed computing. We focus on deterministic distributed algorithms, and study models of computing that are weaker versions of the widely-studied port-numbering model. In the port-numbering model, a node of degree d receives messages through d input ports and sends messages through d output...

We study the complexity of variants of dependence logic defined by
generalized dependency atoms. Let FOC^2 denote two-variable logic with
counting, and let ESO(FOC^2) be the extension of FOC^2 with existential
second-order prenex quantification. We show that for any finite collection A of
atoms that are definable in ESO(FOC^2), the satisfiability p...

We give sound and complete Hilbert-style axiomatizations for propositional dependence logic (PD), modal dependence logic (MDL), and extended modal dependence logic (EMDL) by extending existing axiomatizations for propositional logic and modal logic. In addition, we give novel labeled tableau calculi for PD, MDL, and EMDL. We prove soundness, comple...

We study the validity problem for propositional dependence logic, modal
dependence logic and extended modal dependence logic. We show that the validity
problem for propositional dependence logic is NEXPTIME-complete whereas the
problem for modal dependence logic and extended modal dependence logic is
between NEXPTIME and NEXPTIME^NP.

We study the two-variable fragments D-2 and IF2 of dependence logic and independence-friendly logic. We consider the satisfiability and finite satisfiability problems of these logics and show that for D-2, both problems are NEXPTIME-complete, whereas for IF2, the problems are pi(0)(1) and Sigma(0)(1)-complete, respectively. We also show that D-2 is...

We study the expressive power of various modal logics with team semantics. We show that exactly the properties of teams that are downward closed and closed under team k-bisimulation, for some finite k, are definable in modal logic extended with intuitionistic disjunction. Furthermore, we show that the expressive power of modal logic with intuitioni...

Tarski initiated a logic-based approach to formal geometry that studies first-order structures with a ternary betweenness relation (β) and a quaternary equidistance relation (≡). Tarski established, inter alia, that the first-order (FO) theory of (R^2,β,≡) is decidable. Aiello and van Benthem (2002) conjectured that the FO-theory of expansions of (...

We introduce a new variant of dependence logic (\(\mathcal{D}\)) called Boolean dependence logic (\(\mathcal{BD}\)). In \(\mathcal{BD}\) dependence atoms are of the type =(x
1,...,x
n
,α), where α is a Boolean variable. Intuitively, with Boolean dependence atoms one can express quantification of relations, while standard dependence atoms express qu...

In this paper we extend modal dependence logic \(\mathcal{MDL}\) by allowing dependence atoms of the form dep(ϕ
1,…,ϕ
n
) where ϕ
i
, 1 ≤ i ≤ n, are modal formulas (in \(\mathcal{MDL}\), only propositional variables are allowed in dependence atoms). The reasoning behind this extension is that it introduces a temporal component into modal dependence...

Tarski initiated a logic-based approach to formal geometry that studies
first-order structures with a ternary betweenness relation (\beta) and a
quaternary equidistance relation (\equiv). Tarski established, inter alia, that
the first-order (FO) theory of (R^2,\beta,\equiv) is decidable. Aiello and van
Benthem (2002) conjectured that the FO-theory...

This work presents a classification of weak models of distributed computing. We focus on deterministic distributed algorithms, and we study models of computing that are weaker versions of the widely-studied port-numbering model. In the port-numbering model, a node of degree d receives messages through d input ports and it sends messages through d o...

We study the two-variable fragments D^2 and IF^2 of dependence logic and
independence-friendly logic. We consider the satisfiability and finite
satisfiability problems of these logics and show that for D^2, both problems
are NEXPTIME-complete, whereas for IF^2, the problems are undecidable. We also
show that D^2 is strictly less expressive than IF^...