Related papers: Monadic second order logic as the model companion …

Despite the advanced capabilities of large language models (LLMs), their temporal reasoning ability remains underdeveloped. Prior works have highlighted this limitation, particularly in maintaining temporal consistency when understanding…

Kikyo and Shelah showed that if $T$ is a theory with the Strict Order Property in some first-order language $\mathcal{L}$, then in the expanded language $\mathcal{L}_\sigma := \mathcal{L}\cup\{\sigma\}$ with a new unary function symbol…

Monadic second order logic (MSO2) plays an important role in parameterized complexity due to the Courcelle's theorem. This theorem states that the problem of checking if a given graph has a property specified by a given MSO2 formula can be…

Most autonomous robotic agents use logic inference to keep themselves to safe and permitted behaviour. Given a set of rules, it is important that the robot is able to establish the consistency between its rules, its perception-based…

We present team semantics for two of the most important linear and branching time specification languages, Linear Temporal Logic (LTL) and Computation Tree Logic (CTL). With team semantics, LTL is able to express hyperproperties, which have…

We study trees where each successor set is equipped with some additional structure. We introduce a family of automaton models for such trees and prove their equivalence to certain fixed-point logics. As a consequence we obtain…

It is known that Metric Temporal Logic (MTL) is strictly less expressive than the Monadic First-Order Logic of Order and Metric (FO[<, +1]) when interpreted over timed words; this remains true even when the time domain is bounded a priori.…

We show how to add and eliminate binary preference on plays in Alternating-time Temporal Logic (ATL) with strategy contexts on Concurrent Game Models (CGMs) by means of a translation which preserves satisfaction in models where…

Temporal logics over finite traces have recently seen wide application in a number of areas, from business process modelling, monitoring, and mining to planning and decision making. However, real-life dynamic systems contain a degree of…

We give $\operatorname{CMSO}$-transductions that, given a graph $G$, output its modular decomposition, its split decomposition and its bi-join decomposition. This improves results by Courcelle [Logical Methods in Computer Science, 2006] who…

We use the algebraic framework for languages of infinite trees introduced in [4] to derive effective characterisations of various temporal logics, in particular the logic EF (a fragment of CTL) and its counting variant cEF.

Whereas standard treatments of temporal logic are adequate for closed systems, having no run-time interactions with their environment, they fall short for reactive systems, interacting with their environments through synchronisation of…

In this paper we combine the principled approach to modalities from multimodal type theory (MTT) with the computationally well-behaved realization of identity types from cubical type theory (CTT). The result -- cubical modal type theory…

The importance of intuitionistic temporal logics in Computer Science and Artificial Intelligence has become increasingly clear in the last few years. From the proof-theory point of view, intuitionistic temporal logics have made it possible…

Laminar set systems consist of non-crossing subsets of a universe with set inclusion essentially corresponding to the descendant relationship of a tree, the so-called laminar tree. Laminar set systems lie at the core of many graph…

Hybrid logic extends modal logic with special propositions called nominals, each of which is true at only one state in a model. This enables us to describe some properties of binary relations, such as irreflexivity and anti-symmetry, which…

We consider the problem of learning temporal logic formulas from examples of system behavior. Learning temporal properties has crystallized as an effective mean to explain complex temporal behaviors. Several efficient algorithms have been…

Many modern autonomous systems, particularly multi-agent systems, are time-critical and need to be robust against timing uncertainties. Previous works have studied left and right time robustness of signal temporal logic specifications by…

This paper presents a many-sorted polyadic modal logic that generalizes some of the existing approaches. The algebraic semantics has led us to a many-sorted generalization of boolean algebras with operators, for which we prove the analogue…

Possibilistic computation tree Logic (PoCTL) is one kind of branching temporal logic combined with uncertain information in possibility theory, which was introduced in order to cope with the systematic verification on systems with uncertain…