# Roman KuznetsTU Wien | TU Wien · Institute of Computer Engineering

Roman Kuznets

Ph.D. in Computer Science

## About

57

Publications

4,182

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679

Citations

Citations since 2017

Introduction

Roman Kuznets is currently working at the Institute of Computer Engineering, TU Wien. Roman does research in Logic and Foundations of Mathematics and Distributed Computing. His current projects focus on applications of epistemic logic to distributed systems and interpolation using extensions of sequent calculus.

Additional affiliations

May 2017 - present

June 2014 - April 2019

May 2008 - February 2014

Education

August 2002 - May 2008

## Publications

Publications (57)

Proof-theoretic method has been successfully used almost from the inception of interpolation properties to provide efficient constructive proofs thereof. Until recently, the method was limited to sequent calculi (and their notational variants), despite the richness of generalizations of sequent structures developed in structural proof theory in the...

The goal of this paper is extending to intermediate logics the constructive proof-theoretic method of proving Craig and Lyndon interpolation via hypersequents and nested sequents developed earlier for classical modal logics. While both Jankov and Gödel logics possess hypersequent systems, we show that our method can only be applied to the former. T...

Mathematical logic provides a formal language to describe complex abstract phenomena whereby a finite formula written in a finite alphabet states a property of an object that may even be infinite. Thus, the complexity of the underlying objects is abstracted away to give way for a simple syntactic description, a kind of mathesis universalis. The com...

Justification logics are closely related to modal logics and can be viewed as a refinement of the latter with machinery for justification manipulation. Justifications are represented directly in the language by terms, which can be interpreted as formal proofs in a deductive system, evidence for knowledge, winning strategy in a game, etc. This more...

Combinatorial topology is used in distributed computing to model concurrency and asynchrony. The basic structure in combinatorial topology is the simplicial complex, a collection of subsets called simplices of a set of vertices, closed under containment. Pure simplicial complexes describe message passing in asynchronous systems where all processes...

Knowledge has long been identified as an inherent component of agents' decision-making in distributed systems. However, for agents in fault-tolerant distributed systems with fully byzantine agents, achieving knowledge is, in most cases, unreal-istic. If agents can both lie and themselves be mistaken, then a message received is generally not suffici...

We propose a logic of knowledge for impure simplicial complexes. Impure simplicial complexes represent synchronous distributed systems under uncertainty over which processes are still active (are alive) and which processes have failed or crashed (are dead). Our work generalizes the logic of knowledge for pure simplicial complexes , where all proces...

A modular proof-theoretic framework was recently developed to prove Craig interpolation for normal modal logics based on generalizations of sequent calculi (e.g., nested sequents, hypersequents, and labelled sequents). In this paper, we turn to uniform interpolation, which is stronger than Craig interpolation. We develop a constructive method for p...

We provide a treatement of the intuitionistic diamond modality in the style of justification logic. We introduce a new type of terms, called witness terms, that justify consistency, obtain justification analogs for the constructive modal logics CK, CD, CT, and CS4, and prove the realization theorem for them.

We introduce a novel, semantically inspired method of constructing nested sequent calculi for propositional intermediate logics. Applying recently developed methods for proving Craig interpolation to these nested sequent calculi, we obtain constructive proofs of the interpolation property for most non-trivial interpolable intermediate logics, as we...

In this paper, we provide an epistemic analysis of a simple variant of the fundamental consistent broadcasting primitive for byzantine fault-tolerant asynchronous distributed systems. Our Firing Rebels with Relay (FRR) primitive enables agents with a local preference for acting/not acting to trigger an action (FIRE) at all correct agents, in an all...

A modular proof-theoretic framework was recently developed to prove Craig interpolation for normal modal logics based on generalizations of sequent calculi (e.g., nested sequents, hypersequents, and labelled sequents). In this paper, we turn to uniform interpolation, which is stronger than Craig interpolation. We develop a constructive method for p...

We extend a recently introduced epistemic reasoning framework for multi-agent systems with byzantine faulty asynchronous agents by incorporating features like reliable communication, time-bounded communication, multicasting, synchronous and lockstep synchronous agents. We use this extension framework for analyzing fault detection abilities of synch...

Recently, a detailed epistemic reasoning framework for multi-agent systems with byzantine faulty asynchronous agents and possibly unreliable communication was introduced. We have developed a modular extension framework implemented on top of it, which allows to encode and safely combine additional system assumptions commonly used in the modeling and...

We introduce a novel comprehensive framework for epistemic reasoning in multi-agent systems where agents may behave asynchronously and may be byzantine faulty. Extending Fagin et al.’s classic runs-and-systems framework to agents who may arbitrarily deviate from their protocols, it combines epistemic and temporal logic and incorporates fine-grained...

Causality is an important concept both for proving impossibility results and for synthesizing efficient protocols in distributed computing. For asynchronous agents communicating over unreliable channels, causality is well studied and understood. This understanding, however, relies heavily on the assumption that agents themselves are correct and rel...

Causal analysis of asynchronous distributed multi-agent systems

Causality is an important concept both for proving impossibility results and for synthesizing efficient protocols in distributed computing. For asynchronous agents communicating over unreliable channels, causality is well studied and understood. This understanding, however, relies heavily on the assumption that agents themselves are correct and rel...

We develop multi-conclusion nested sequent calculi for the fifteen logics of the intuitionistic modal cube between IK and IS5. The proof of cut-free completeness for all logics is provided both syntactically via a Maehara-style translation and semantically by constructing an infinite birelational countermodel from a failed proof search. Interesting...

We present an extension incorporating Byzantine agents into the epistemic runs-and-systems framework for modeling distributed systems introduced by Fagin et al. [FHMV95]. Our framework relies on a careful separation of concerns for various actors involved in the evolution of a message-passing distributed system: the agents' protocols, the underlyin...

Interpolation is a fundamental logical property with applications
in mathematics, computer science, and artificial intelligence. In
this paper, we develop a general method of translating a semantic description
of modal logics via Kripke models into a constructive proof
of the Lyndon interpolation property (LIP) via labelled sequents. Using
this met...

In this paper, we describe a novel constructive method of proving the Craig interpolation property (CIP) based on cut-free hypersequent calculi and apply the method to prove the CIP for the modal logic S5.

We introduce a new Gentzen-style framework of grafted hypersequents that combines the formalism of nested sequents with that
of hypersequents. To illustrate the potential of the framework, we present novel calculi for the modal logics K5 and KD5, as well as for extensions of the modal logics K and KD with the axiom for shift reflexivity. The latter...

Artemov established an arithmetical interpretation for the Logics of Proofs LPCS, which yields a classical provability semantics for the modal logic S4. The Logics of Proofs are parameterized by so-called constant specifications CS, stating which axioms can be used in the reasoning process, and the arithmetical interpretation relies on constant spe...

In two recent papers, we outlined how the proof-theoretic method of proving the Craig interpolation property can be extended from sequents to nested sequents (joint work with Fitting) and hypersequents. However, these results have been presented separately and using notation fine tuned to each of the formalisms, which obscures the common idea behin...

Justification logics were introduced by Artemov in 1995 to provide intuitionistic logic with a classical provability semantics, a problem originally posed by Gödel. Justification logics are refinements of modal logics and formally connected to them by so-called realization theorems. A constructive proof of a realization theorem typically relies on...

The main method of proving the Craig Interpolation Property (CIP) constructively uses cut-free sequent proof systems. Until now, however, no such method has been known for proving the CIP using more general sequent-like proof formalisms, such as hypersequents, nested sequents, and labelled sequents. In this paper, we start closing this gap by prese...

Modal public announcement logics study how beliefs change after public announcements. However, these logics cannot express the reason for a new belief. Justification logics fill this gap since they can formally represent evidence and justifications for an agent's belief. We present OPAL(K) and JPAL(K), two alternative justification counterparts of...

Logical theories for representing knowledge are often plagued by the so-called Logical Omniscience Problem. The problem stems from the clash between the desire to model rational agents, which should be capable of simple logical inferences, and the fact that any logical inference, however complex, almost inevitably consists of inference steps that a...

Justification logics are propositional modal-like logics that instead of statements A is known include statements of the form A is known for reason t where the term t can represent an informal justification for A or a formal proof of A. In our present work, we introduce model-theoretic tools, namely: filtrations and a certain form of generated subm...

We introduce a justification logic with a novel constructor for evidence terms, according to which the new information itself serves as evidence for believing it. We provide a sound and complete axiomatization for belief expansion and minimal change and explain how the minimality can be graded according to the strength of reasoning. We also provide...

Justification logics are refinements of modal logics, where justification terms replace modalities. Modal and justification logics are connected via the so-called realization theorems. We develop a general constructive method of proving the realization of a modal logic in an appropriate justification logic by means of cut-free modal nested sequent...

An ontologically transparent semantics for justifications that interprets justifications as sets of formulas they justify has been recently presented by Artemov. However, this semantics of modular models has only been studied for the case of the basic justification logic J, corresponding to the modal logic K. It has been left open how to extend and...

Justification Logic studies epistemic and provability phenomena by introducing justi-fications/proofs into the language in the form of justification terms. Pure justification logics serve as counterparts of traditional modal epistemic logics, and hybrid logics combine epistemic modalities with justification terms. The computational complex-ity of p...

Justification logic is an epistemic framework that provides a way to express explicit justifications for the agent’s belief. In this paper, we present OPAL, a dynamic justification logic that includes term operators to reflect public announcements on the level of justifications. We create dynamic epistemic semantics for OPAL. We also elaborate on t...

Justification logics are epistemic logics that explicitly include justifications for the agents' knowledge. We develop a multi-agent justification logic with evidence terms for individual agents as well as for common knowledge. We define a Kripke-style semantics that is similar to Fitting's semantics for the Logic of Proofs LP. We show the soundnes...

Justification Logic is a framework for reasoning about evidence and justification. Public Announcement Logic is a framework for reasoning about belief changes caused by public announcements. This paper develops JPAL, a dynamic justification logic of public announcements that corresponds to the modal theory of public announcements due to Gerbrandy a...

Justification logics are refinements of modal logics where modalities are replaced by justification terms. They are connected to modal logics via so-called realization theorems. We present a syntactic proof of a single realization theorem that uniformly connects all the normal modal logics formed from the axioms d, t, b, 4, and 5 with their justifi...

Justification logics [Art08] are essentially refined analogs of modal epistemic logics. Whereas a modal epistemic logic uses the formula F to indicate that F is known to be true, a justification logic uses t : F instead, where t is a term that describes a 'justification' or proof of F . The structure of justification terms t depends on which modal...

It is not clear what a system for evidence-based common knowledge should look like if common knowledge is treated as a greatest fixed point. This paper is a preliminary step towards such a system. We argue that the standard induction rule is not well suited to axiomatize evidence-based common knowledge. As an alternative, we study two different ded...

Justification logics are epistemic logics that explicitly include justifications for the agents' knowledge. We develop a multi-agent justification logic with evidence terms for individual agents as well as for common knowledge. We define a Kripke-style semantics that is similar to Fitting's semantics for the Logic of Proofs LP. We show the soundnes...

This paper is devoted to the study of self-referential proofs and/or justifications, i.e., valid proofs that prove statements about these same proofs. The goal is to investigate whether such self-referential justifications are present in the reasoning described by standard modal epistemic logics such as S4. We argue that the modal language by itsel...

The logical omniscience feature assumes that an epistemic agent knows,all logical consequences of her assumptions. This paper offers a general theoretical framework, that views logical omniscience as a computational complexity problem. We suggest the following approach: we assume that the knowledge, of an agent is represented by an epistemic logica...

The Logic of Proofs LP, introduced by Artemov, encodes the same reasoning as the modal logic S4 using proofs explicitly present in the language. In particular, Artemov showed that three operations on proofs (application , positive introspection !, and sum +) are sufficient to mimic provability concealed in S4 modality. While the first two operation...

Logics J, JD, JT, J4, JD4, and LP are explicit counterparts of modal epistemic logics K, D, T, K4, D4, and S4 respectively (see [2, 1] for more details). An upper bound of Σ p 2 for the satisfiability problem in these justification logics was announced in [3]. The algorithm was essentially a propositional tableau procedure (though not presented as...

Justification Logic studies epistemic and provability phenomena by introducing justifications/proofs into the language in the form of justification terms. Pure justification logics serve as counterparts of traditional modal epistemic logics, and hybrid logics combine epistemic modalities with justification terms. The computational complexity of pur...

The principal result of Justification Logic is the Realization Theorem, which states that behind major epistemic modal logics there are corresponding systems of evidence/justification terms sufficient for reading all provable knowledge assertions as statements about justifications. A knowledge/belief modality is self-referential if there are modal...

Justification Logic is an emerging field that studies provability, knowledge, and belief via explicit proofs or justifications that are part of the language. There exist many justification logics closely related to modal epistemic logics of knowledge and belief. Instead of modality □ in pure justification logics, or in addition to modality □ in hyb...

The problem of the identity criteria for proofs can be traced to Hilbert and Prawitz. One of the approaches, which uses the concept of generality of proofs, was suggested in 1968 by Lambek. Following his ideas, we propose a language and a logic to represent Hilbert-style proofs for classical propositional logic by adapting the Logic of Proofs (LP)...

The Hintikka-style modal logic approach to knowledge contains a well-known defect of logical omniscience, i.e., the unrealistic feature that an agent knows all logical consequences of her assumptions. In this paper, we suggest the following Logical Omniscience Test (LOT): an epistemic system E is not logically omniscient if for any valid in E knowl...

A system of evidence-based knowledge S4LP was recently proposed by Artemov and Nogina. It combines epistemic modal operator with explicit evidence represented by evidence terms similar to those of Artemov's Logic of Proofs. This logic S4LP and its generalizations promise a new approach to common-knowledge and to the logical omniscience problem. In...

Artemov's logic of proofs LP is a complete calculus of propositions and proofs, which is now becoming a foundation for the evidence-based approach to reasoning about knowledge. Additional atoms in LP have form t:F, read as “t is a proof of F” (or, more generally, as “t is an evidence for F”) for an appropriate system of terms t called proof polynom...

Explicit modal logic was introduced by S. Artemov. Whereas the traditional modal logic uses atoms ☐F with a possible semantics “F is provable”, the explicit modal logic deals with atoms of form t:F, where t is a proof polynomial denoting a specific proof of a formula F. Artemov found the explicit modal logic LP in this new format and built an algor...

## Projects

Projects (6)

We investigate the proof theory of important families of logics that are variants and generalizations of modal logics. These logics have been applied in various areas of mathematics, epistemology, philosophy, and computer science (e.g. conditional logics in hypothetical and plausible reasoning, epistemic logics in reasoning about knowledge, and bunched implication logics in separation and sharing of resources).
Several types of proof systems (calculi) have been proposed for these logics falling into two categories: internal calculi, whose basic objects can be read as formulas of the logic (e.g. hypersequent and nested calculus), and external calculi, whose basic objects are formulas of a more expressive language which partially encode the logic's semantics (e.g. labelled and display calculi). Internal and external calculi possess different properties: the former are more suitable for establishing properties such as termination, interpolation, and optimal complexity, while external calculi are easier to find and permit easier proofs of completeness, cut admissibility, and countermodel generation (from a terminating calculus).
Internal and external calculi have been introduced essentially as two independent, occasionally opposing, streams in proof theory with varying degrees of success. For certain classes of logics, no internal calculi are known, while for others, optimal external calculi are known. An integrated and systematic study of internal and external calculi has not been carried out in the 30 years of research in this area. This project will address this gap, focusing on modal and related logics, where the status of many meta-logical properties concerning various classes of logics is open. We will systematically study the interrelationships in order to facilitate the exchange of results between the two types of calculi (e.g. interpolation, semantic completeness, and countermodel generation) and to provide new tools to tackle open problems concerning decidability, conservativity and axiomatisations.
Link to Project Website: https://ticamore.logic.at/

Study Reasoning about Knowledge in Byzantine Distributed Systems