Related papers: Guarded Successor: A Novel Temporal Logic
We consider first-order logic over the subword ordering on finite words, where each word is available as a constant. Our first result is that the $\Sigma_1$ theory is undecidable (already over two letters). We investigate the decidability…
Quantified CTL (QCTL) is a well-studied temporal logic that extends CTL with quantification over atomic propositions. It has recently come to the fore as a powerful intermediary framework to study logics for strategic reasoning. We extend…
Sound and complete axiomatizations are provided for a number of different logics involving modalities for knowledge and time. These logics arise from different choices for various parameters. All the logics considered involve the discrete…
In this article, we give a precise mathematical meaning to `linear? time' that matches experimental behaviour of the algorithm. The sorting algorithm is not our own, it is a variant of radix sort with counting sort as a subroutine. The true…
Reasoning about program equivalence in imperative languages is notoriously challenging, as the presence of states (in the form of variable stores) fundamentally increases the observational power of program terms. The key desideratum for any…
Control synthesis from temporal logic specifications has gained popularity in recent years. In this paper, we use a model predictive approach to control discrete time linear systems with additive bounded disturbances subject to constraints…
It is well-known that every first-order property on words is expressible using at most three variables. The subclass of properties expressible with only two variables is also quite interesting and well-studied. We prove precise structure…
Recently, the separated fragment (SF) of first-order logic has been introduced. Its defining principle is that universally and existentially quantified variables may not occur together in atoms. SF properly generalizes both the…
We propose a new graph-based spatial temporal logic for knowledge representation and automated reasoning in this paper. The proposed logic achieves a balance between expressiveness and tractability in applications such as cognitive robots.…
In the wake of the recent resurgence of the Datalog language of databases, together with its extensions for ontological reasoning settings, this work aims to bridge the gap between the theoretical studies of DatalogMTL (Datalog extended…
The theory of finite term algebras provides a natural framework to describe the semantics of functional languages. The ability to efficiently reason about term algebras is essential to automate program analysis and verification for…
While large language models (LLMs) have achieved impressive performance in generating fluent and realistic text, controlling the generated text so that it exhibits properties such as safety, factuality, and non-toxicity remains challenging.…
Model checking linear-time properties expressed in first-order logic has non-elementary complexity, and thus various restricted logical languages are employed. In this paper we consider two such restricted specification logics, linear…
We show that for any $i > 0$, it is decidable, given a regular language, whether it is expressible in the $\Sigma_i[<]$ fragment of first-order logic FO[<]. This settles a question open since 1971. Our main technical result relies on the…
In this paper, our aim is to briefly survey and articulate the logical and philosophical foundations of using (first-order) logic to represent (probabilistic) knowledge in a non-technical fashion. Our motivation is three fold. First, for…
Topos theory has been suggested by Doring and Isham as an alternative mathematical structure with which to formulate physical theories. In particular it has been used to reformulate standard quantum mechanics in such a way that a novel type…
We prove that the form of conditional independence at play in database theory and independence logic is reducible to the first-order dividing calculus in the theory of atomless Boolean algebras. This establishes interesting connections…
In this paper, we introduce a novel team semantics of LTL inspired by inquisitive logic. The main features of the resulting logic, we call InqLTL, are the intuitionistic interpretation of implication and the Boolean semantics of…
We consider G\"odel temporal logic ($\sf GTL$), a variant of linear temporal logic based on G\"odel--Dummett propositional logic. In recent work, we have shown this logic to enjoy natural semantics both as a fuzzy logic and as a…
Representing time is crucial for cyber-physical systems and has been studied extensively in the Situation Calculus. The most commonly used approach represents time by adding a real-valued fluent $\mathit{time}(a)$ that attaches a time point…