Related papers: Rank logic is dead, long live rank logic!
We investigate the decidability of model-checking logics of time, knowledge and probability, with respect to two epistemic semantics: the clock and synchronous perfect recall semantics in partially observed discrete-time Markov chains.…
In this article, we study parameterized complexity theory from the perspective of logic, or more specifically, descriptive complexity theory. We propose to consider parameterized model-checking problems for various fragments of first-order…
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 introduce a weighted linear dynamic logic (weighted LDL for short) and show the expressive equivalence of its formulas to weighted rational expressions. This adds a new characterization for recognizable series to the fundamental…
Recently, $\alpha$-Rank, a graph-based algorithm, has been proposed as a solution to ranking joint policy profiles in large scale multi-agent systems. $\alpha$-Rank claimed tractability through a polynomial time implementation with respect…
Recent advances in reasoning with large language models (LLMs) have demonstrated strong performance on complex mathematical tasks, including combinatorial optimization. Techniques such as Chain-of-Thought and In-Context Learning have…
We present a novel asynchronous hyper linear time temporal logic named LPrL (Linear Time Predicate Logic) and establish its basic theory. LPrL is a natural first order extension of LTL (Linear time temporal logic), in which the predicates…
Over the past few decades, non-monotonic reasoning has developed to be one of the most important topics in computational logic and artificial intelligence. Different ways to introduce non-monotonic aspects to classical logic have been…
Practitioners designing reinforcement learning policies face a fundamental challenge: translating intended behavioral objectives into representative reward functions. This challenge stems from behavioral intent requiring simultaneous…
Propositional temporal logic over the real number time flow is finitely axiomatisable, but its first-order counterpart is not recursively axiomatisable. We study the logic that combines the propositional axiomatisation with the usual axioms…
We continue the investigation of parameterized extensions of Linear Temporal Logic (LTL) that retain the attractive algorithmic properties of LTL: a polynomial space model checking algorithm and a doubly-exponential time algorithm for…
The existence of a polynomial pivot rule for the simplex method for linear programming, policy iteration for Markov decision processes, and strategy improvement for parity games each are prominent open problems in their respective fields.…
Fixed-parameter tractability analysis and scheduling are two core domains of combinatorial optimization which led to deep understanding of many important algorithmic questions. However, even though fixed-parameter algorithms are appealing…
Given a linear subspace of $n \times n$ matrices over $\mathbb F_{2^r}$ that is promised to contain a matrix of rank $1$, we prove that it is hard to find a matrix of rank $n^{o(1/\log \log n)}$, assuming NP doesn't have sub-exponential…
Argumentation frameworks, consisting of arguments and an attack relation representing conflicts, are fundamental for formally studying reasoning under conflicting information. We use methods from mathematical logic, specifically…
Probabilistic systems are an important theme in AI domain. As the specification language, the logic PCTL is now the default logic for reasoning about probabilistic properties. In this paper, we present a natural and succinct probabilistic…
We propose a novel logic, called Frame Logic (FL), that extends first-order logic (with recursive definitions) using a construct Sp(.) that captures the implicit supports of formulas -- the precise subset of the universe upon which their…
The paper is focused on temporal logics for the description of the behaviour of real-time pushdown reactive systems. The paper is motivated to bridge tractable logics specialized for expressing separately dense-time real-time properties and…
Metric Temporal Logic (MTL) and Timed Propositional Temporal Logic (TPTL) extend Linear Temporal Logic (LTL) for real-time constraints, with MTL using time-bounded modalities and TPTL employing freeze quantifiers. Satisfiability for both is…
The logic PJ is a probabilistic logic defined by adding (non-iterated) probability operators to the basic justification logic J. In this paper we establish upper and lower bounds for the complexity of the derivability problem in the logic…