Related papers: A sound and complete axiomatization for Dynamic To…
The paper presents probabilistic extensions of interval temporal logic (ITL) and duration calculus (DC) with infinite intervals and complete Hilbert-style proof systems for them. The completeness results are a strong completeness theorem…
Signal Temporal Logic (STL) has gained popularity in recent years as a specification language for cyber-physical systems, especially in robotics. Beyond being expressive and easy to understand, STL is appealing because the synthesis…
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…
The analysis of complex dynamic systems is a core research topic in formal methods and AI, and combined modelling of systems with data has gained increasing importance in applications such as business process management. In addition,…
Many classical planning frameworks are built on first-order languages. The first-order expressive power is desirable for compactly representing actions via schemas, and for specifying quantified conditions such as $\neg\exists…
A logic-enriched type theory (LTT) is a type theory extended with a primitive mechanism for forming and proving propositions. We construct two LTTs, named LTTO and LTTO*, which we claim correspond closely to the classical predicative…
We introduce proper display calculi for basic monotonic modal logic,the conditional logic CK and a number of their axiomatic extensions. These calculi are sound, complete, conservative and enjoy cut elimination and subformula property. Our…
Although Dynamic Epistemic Logic (DEL) is an influential logical framework for representing and reasoning about information change, little is known about the computational complexity of its associated decision problems. In fact, we only…
This paper introduces robust differential dynamic logic (a fragment of differential dynamic logic) to specify and reason about robust hybrid systems. Practically meaningful syntactic restrictions naturally ensure that definable properties…
Deontic logic is a very well researched branch of mathematical logic and philosophy. Various kinds of deontic logics are discussed for different application domains like argumentation theory, legal reasoning, and acts in multi-agent…
This paper presents \tdl, a typed feature-based representation language and inference system. Type definitions in \tdl\ consist of type and feature constraints over the boolean connectives. \tdl\ supports open- and closed-world reasoning…
Hybrid logic is one of the extensions of modal logic. The many-dimensional product of hybrid logic is called hybrid product logic (HPL). We construct a sound and complete tableau calculus for two-dimensional HPL. Also, we made a tableau…
LTL3 is a multi-valued variant of Linear-time Temporal Logic for runtime verification applications. The semantic descriptions of LTL3 in previous work are given only in terms of the relationship to conventional LTL. Our approach, by…
Definite descriptions are expressions of the form "the unique $x$ satisfying property $C$," which allow reference to objects through their distinguishing characteristics. They play a crucial role in ontology and query languages, offering an…
This book introduces a temporal type theory, the first of its kind as far as we know. It is based on a standard core, and as such it can be formalized in a proof assistant such as Coq or Lean by adding a number of axioms. Well-known…
Recent years have seen an increasing use of Signal Temporal Logic (STL) as a formal specification language for symbolic control, due to its expressiveness and closeness to natural language. Furthermore, STL specifications can be encoded as…
In the Declarative Networking paradigm, Datalog-like languages are used to express distributed computations. Whereas recently formal operational semantics for these languages have been developed, a corresponding declarative semantics has…
We study the classical problem of verifying programs with respect to formal specifications given in the linear temporal logic (LTL). We first present novel sound and complete witnesses for LTL verification over imperative programs. Our…
We introduce Parametric Linear Dynamic Logic (PLDL), which extends Linear Dynamic Logic (LDL) by temporal operators equipped with parameters that bound their scope. LDL was proposed as an extension of Linear Temporal Logic (LTL) that is…
Many forms of dependence manifest themselves over time, with behavior of variables in dynamical systems as a paradigmatic example. This paper studies temporal dependence in dynamical systems from a logical perspective, by enriching a…