arXiv subjects

Malvin Gattinger

Publications and source records attributed to Malvin Gattinger.

11 recordsLinked to original sources

arXiv2026

Propositional Dynamic Logic has Craig Interpolation: a tableau-based proof

We show that Propositional Dynamic Logic (PDL) has the Craig Interpolation Property. This question has been open for many years. Three proof attempts were published, but later criticized in the literature or retracted. Our proof is based on the main ideas from Borzechowski (1988, master thesis). We define a cyclic tableau system for PDL with a loading mechanism to recognize successful repeats. For this system, we show soundness and completeness via a game. To show interpolation, we modify Maehara's method to work for tableaux with repeats: we first define pre-interpolants at each node, and then use a quasi-tableau to define interpolants for clusters (strongly connected components). In different terms, our method solves the fixpoint equations that characterize the desired interpolants, and the method ensures that the solutions to these equations can be expressed within PDL. The proof is constructive and we show how to compute interpolants. We also make available a Haskell implementation of the proof system that provides interpolants. Lastly, we mention ongoing work to formally verify this proof in the interactive theorem prover Lean, and several questions for future work.

cs.LO↗

arXiv2026

Proceedings of the Sixteenth International Conference on Advances in Modal Logic

Advances in Modal Logic (AiML) was founded in 1995 as an initiative devoted to presenting an up-to-date picture of research in modal logic and its many applications. It combines a conference series with volumes arising from the conferences, and has become the flagship international forum for work on all aspects of modal logic. Over the past three decades, AiML has both recorded and helped shape developments across the field, bringing together semantic, proof-theoretic, algebraic, topological, computational, philosophical, and applied perspectives on modal and related logics. Exactly thirty years after the first AiML conference, AiML 2026, the sixteenth conference in the series, is organized by the Institute of Logic, Language and Computation (ILLC) of the University of Amsterdam. The conference takes place in Amsterdam, the Netherlands, from 29 June to 3 July 2026. This volume contains abstracts of invited talks and full papers accepted for the conference. Beginning with AiML 2026, the proceedings are published open access via Electronic Proceedings in Theoretical Computer Science (EPTCS).

cs.LO↗

arXiv2026

Self-Correcting Gossip Protocols

We investigate self-correcting gossip protocols with errors. In distributed computing, protocols with errors have been widely investigated in temporal epistemic logics. Instead, we propose a dynamic epistemic logic. We show how to correct transmission errors due to faulty messages without a central authority coordinating protocol execution, how this affects optimality, and how this compares to bounded memory and full information protocols.

cs.LO↗

arXiv2025

Comparing State-Representations for DEL Model Checking

Model checking with the standard Kripke models used in (Dynamic) Epistemic Logic leads to scalability issues. Hence alternative representations have been developed, in particular symbolic structures based on Binary Decision Diagrams (BDDs) and succinct models based on mental programs. While symbolic structures have been shown to perform well in practice, their theoretical complexity was not known so far. On the other hand, for succinct models model checking is known to be PSPACE-complete, but no implementations are available. We close this gap and directly relate the two representations. We show that model checking DEL on symbolic structures encoded with BDDs is also PSPACE-complete. In fact, already model checking Epistemic Logic without dynamics is PSPACE-complete on symbolic structures. We also provide direct translations between BDDs and mental programs. Both translations yield exponential outputs. For the translation from mental programs to BDDs we show that no small translation exists. For the other direction we conjecture the same.

cs.LO↗

arXiv2025

Virtual Group Knowledge and Group Belief in Topological Evidence Models (Extended Version)

We study notions of (virtual) group knowledge and group belief within multi-agent evidence models, obtained by extending the topological semantics of evidence-based belief and fallible knowledge from individuals to groups. We completely axiomatize and show the decidability of the logic of ("hard" and "soft") group evidence, and do the same for an especially interesting fragment of it: the logic of group knowledge and group belief. We also extend these languages with dynamic evidence-sharing operators, and completely axiomatize the corresponding logics, showing that they are co-expressive with their static bases.

cs.AI↗

arXiv2023

Exploiting Asymmetry in Logic Puzzles: Using ZDDs for Symbolic Model Checking Dynamic Epistemic Logic

Binary decision diagrams (BDDs) are widely used to mitigate the state-explosion problem in model checking. A variation of BDDs are Zero-suppressed Decision Diagrams (ZDDs) which omit variables that must be false, instead of omitting variables that do not matter. We use ZDDs to symbolically encode Kripke models used in Dynamic Epistemic Logic, a framework to reason about knowledge and information dynamics in multi-agent systems. We compare the memory usage of different ZDD variants for three well-known examples from the literature: the Muddy Children, the Sum and Product puzzle and the Dining Cryptographers. Our implementation is based on the existing model checker SMCDEL and the CUDD library. Our results show that replacing BDDs with the right variant of ZDDs can significantly reduce memory usage. This suggests that ZDDs are a useful tool for model checking multi-agent systems.

cs.LO↗

arXiv2022

Everyone Knows that Everyone Knows: Gossip Protocols for Super Experts

A gossip protocol is a procedure for sharing secrets in a network. The basic action in a gossip protocol is a pairwise message exchange (telephone call) wherein the calling agents exchange all the secrets they know. An agent who knows all secrets is an expert. The usual termination condition is that all agents are experts. Instead, we explore protocols wherein the termination condition is that all agents know that all agents are experts. We call such agents super experts. We also investigate gossip protocols that are common knowledge among the agents. Additionally, we model that agents who are super experts do not make and do not answer calls, and that this is common knowledge. We investigate conditions under which protocols terminate, both in the synchronous case, where there is a global clock, and in the asynchronous case, where there is not. We show that a commonly known protocol with engaged agents may terminate faster than the same commonly known protocol without engaged agents.

cs.AI↗

arXiv2019

Towards Symbolic Factual Change in DEL

We extend symbolic model checking for Dynamic Epistemic Logic (DEL) with factual change. Our transformers provide a compact representation of action models with pre- and postconditions, for both S5 and the general case. The method can be implemented using binary decision diagrams and we expect it to improve model checking performance. As an example we give a symbolic representation of the Sally-Anne false belief task.

cs.LO↗

arXiv2019

Strengthening Gossip Protocols using Protocol-Dependent Knowledge

Distributed dynamic gossip is a generalization of the classic telephone problem in which agents communicate to share secrets, with the additional twist that also telephone numbers are exchanged to determine who can call whom. Recent work focused on the success conditions of simple protocols such as "Learn New Secrets" (LNS) wherein an agent a may only call another agent b if a does not know b's secret. A protocol execution is successful if all agents get to know all secrets. On partial networks these protocols sometimes fail because they ignore information available to the agents that would allow for better coordination. We study how epistemic protocols for dynamic gossip can be strengthened, using epistemic logic as a simple protocol language with a new operator for protocol-dependent knowledge. We provide definitions of different strengthenings and show that they perform better than LNS, but we also prove that there is no strengthening of LNS that always terminates successfully. Together, this gives us a better picture of when and how epistemic coordination can help in the dynamic gossip problem in particular and distributed systems in general.

cs.LO↗

arXiv2019

How to Agree without Understanding Each Other: Public Announcement Logic with Boolean Definitions

In standard epistemic logic, knowing that p is the same as knowing that p is true, but it does not say anything about understanding p or knowing its meaning. In this paper, we present a conservative extension of Public Announcement Logic (PAL) in which agents have knowledge or belief about both the truth values and the meanings of propositions. We give a complete axiomatization of PAL with Boolean Definitions and discuss various examples. An agent may understand a proposition without knowing its truth value or the other way round. Moreover, multiple agents can agree on something without agreeing on its meaning and vice versa.

cs.LO↗

arXiv2016

Knowing Values and Public Inspection

We present a basic dynamic epistemic logic of "knowing the value". Analogous to public announcement in standard DEL, we study "public inspection", a new dynamic operator which updates the agents' knowledge about the values of constants. We provide a sound and strongly complete axiomatization for the single and multi-agent case, making use of the well-known Armstrong axioms for dependencies in databases.

cs.LO↗