Related papers: A logic with temporally accessible iteration
Standpoint extensions of knowledge representation formalisms have been recently introduced as a means to incorporate multi-perspective modelling and reasoning through modal operators that attribute pieces of knowledge to specific entities…
Linear Temporal Logic (LTL) is one of the most popular temporal logics, that comes into play in a variety of branches of computer science. Among the various reasons of its widespread use there are its strong foundational properties: LTL is…
Linear Temporal Logic over finite traces ($\text{LTL}_f$) is a widely used formalism with applications in AI, process mining, model checking, and more. The primary reasoning task for $\text{LTL}_f$ is satisfiability checking; yet, the…
Logical reasoning is a key task for artificial intelligence due to it's role in major downstream tasks such as Question Answering, Summarization. Recent methods in improving the reasoning ability of LLMs fall short in correctly converting a…
We propose extending Alternating-time Temporal Logic (ATL) by an operator <i refines-to G> F to express that agent i can distribute its powers to a set of sub-agents G in a way which satisfies ATL condition f on the strategic ability of the…
This paper proposes a specification-guided framework for control of nonlinear systems with linear temporal logic (LTL) specifications. In contrast with well-known abstraction-based methods, the proposed framework directly characterizes the…
First-order logic is known to have limited expressive power over finite structures. It enjoys in particular the locality property, which states that first-order formulae cannot have a global view of a structure. This limitation ensures on…
We use the method of monotone iterations to obtain fixed point and coupled fixed point results for mixed monotone operators in the setting of partially ordered sets, with no additional assumptions on the partial order and with no…
We argue that in some KR applications, we want to quantify over sets of concepts formally represented by symbols in the vocabulary. We show that this quantification should be distinguished from second-order quantification and…
Linear temporal logic (LTL) is a powerful language for task specification in reinforcement learning, as it allows describing objectives beyond the expressivity of conventional discounted return formulations. Nonetheless, recent works have…
Logical formalisms for reasoning about relations between spatial regions play a fundamental role in geographical information systems, spatial and constraint databases, and spatial reasoning in AI. In analogy with Halpern and Shoham's modal…
This paper relates the well-known Linear Temporal Logic with the logic of propositional schemata introduced by the authors. We prove that LTL is equivalent to a class of schemata in the sense that polynomial-time reductions exist from one…
First-order logic (FO) can express many algorithmic problems on graphs, such as the independent set and dominating set problem, parameterized by solution size. On the other hand, FO cannot express the very simple algorithmic question of…
Until recently, First-Order Temporal Logic (FOTL) has been little understood. While it is well known that the full logic has no finite axiomatisation, a more detailed analysis of fragments of the logic was not previously available. However,…
Well-founded fixed points have been used in several areas of knowledge representation and reasoning and to give semantics to logic programs involving negation. They are an important ingredient of approximation fixed point theory. We study…
We investigate infinitary wellfounded systems for linear logic with fixed points, with transfinite branching rules indexed by some closure ordinal $\alpha$ for fixed points. Our main result is that provability in the system for some…
Higher-Order Fixpoint Logic (HFL) is a hybrid of the simply typed \lambda-calculus and the modal \lambda-calculus. This makes it a highly expressive temporal logic that is capable of expressing various interesting correctness properties of…
A logic formalism is presented which increases the expressive power of the ID/LP format of GPSG by enlarging the inventory of ordering relations and extending the domain of their application to non-siblings. This allows a concise, modular…
We consider a specific class of tree structures that can represent basic structures in linguistics and computer science such as XML documents, parse trees, and treebanks, namely, finite node-labeled sibling-ordered trees. We present…
In this article we study linear temporal logics with team semantics (TeamLTL) that are novel logics for defining hyperproperties. We define Kamp-type translations of these logics into fragments of first-order team logic and second-order…