Related papers: Quantifying over Trees in Monadic Second-Order Log…

Theory of tree transducers provides a foundation for understanding expressiveness and complexity of analysis problems for specification languages for transforming hierarchically structured data such as XML documents. We introduce streaming…

The first-order theory of finite and infinite trees has been studied since the eighties, especially by the logic programming community. Following Djelloul, Dao and Fr\"uhwirth, we consider an extension of this theory with an additional…

Separation Logic is a widely used formalism for describing dynamically allocated linked data structures, such as lists, trees, etc. The decidability status of various fragments of the logic constitutes a long standing open problem. Current…

In the last years, enumeration algorithms with bounded delay have attracted a lot of attention for several data management tasks. Given a query and the data, the task is to preprocess the data and then enumerate all the answers to the query…

Temporal logics are widely used by the Formal Methods and AI communities. Linear Temporal Logic is a popular temporal logic and is valued for its ease of use as well as its balance between expressiveness and complexity. LTL is equivalent in…

Characterisations theorems serve as important tools in model theory and can be used to assess and compare the expressive power of temporal languages used for the specification and verification of properties in formal methods. While complete…

In this work we introduce new generalised quantifiers which allow us to express the Rabin-Mostowski index of automata. Our main results study expressive power and decidability of the monadic second-order (MSO) logic extended with these…

We study Linear Temporal Logic Modulo Theories over Finite Traces (LTLfMT), a recently introduced extension of LTL over finite traces (LTLf) where propositions are replaced by first-order formulas and where first-order variables referring…

We study a new extension of the weak MSO logic, talking about boundedness. Instead of a previously considered quantifier U, expressing the fact that there exist arbitrarily large finite sets satisfying a given property, we consider a…

The satisfiability problem of the branching time logic CTL is studied in terms of computational complexity. Tight upper and lower bounds are provided for each temporal operator fragment. In parallel, the minimal model size is studied with a…

Probabilistic search algorithms, such as Monte Carlo Tree Search (MCTS), have proven very effective in solving sequential decision-making tasks under uncertainty. However, interpreting asymmetric search trees that incorporate bandit-based…

We characterise the sentences in Monadic Second-order Logic (MSO) that are over finite structures equivalent to a Datalog program, in terms of an existential pebble game. We also show that for every class C of finite structures that can be…

Hypertrace logic is a sorted first-order logic with separate sorts for time and execution traces. Its formulas specify hyperproperties, which are properties relating multiple traces. In this work, we extend hypertrace logic by introducing…

Suitable extensions of the monadic second-order theory of k successors have been proposed in the literature to capture the notion of time granularity. In this paper, we provide the monadic second-order theories of downward unbounded layered…

Logic languages based on the theory of rational, possibly infinite, trees have much appeal in that rational trees allow for faster unification (due to the safe omission of the occurs-check) and increased expressivity (cyclic terms can…

This paper studies the logical properties of a very general class of infinite ranked trees, namely those generated by higher-order recursion schemes. We consider, for both monadic second-order logic and modal mu-calculus, three main…

Permutations can be viewed as pairs of linear orders, or more formally as models over a signature consisting of two binary relation symbols. This approach was adopted by Albert, Bouvel and F\'eray, who studied the expressibility of…

We introduce a new family of temporal logics intended for specifications in motion planning (MP). It builds upon the signal temporal logic (STL), which is a linear-time logic over real-valued signals that possess quantitative semantics and…

Recent advances in reasoning with large language models (LLMs) have shown the effectiveness of Monte Carlo Tree Search (MCTS) for generating high quality intermediate trajectories, particularly in math and symbolic domains. Inspired by…

We investigate ontology-based data access to temporal data. We consider temporal ontologies given in linear temporal logic LTL interpreted over discrete time (Z,<). Queries are given in LTL or MFO(<), monadic first-order logic with a…