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Temporal logics over finite traces have recently seen wide application in a number of areas, from business process modelling, monitoring, and mining to planning and decision making. However, real-life dynamic systems contain a degree of…

This paper introduces Logical Credal Networks, an expressive probabilistic logic that generalizes many prior models that combine logic and probability. Given imprecise information represented by probability bounds and conditional…

In this note, we provide complexity characterizations of model checking multi-pushdown systems. Multi-pushdown systems model recursive concurrent programs in which any sequential process has a finite control. We consider three standard…

Repeated recursion unfolding is a new approach that repeatedly unfolds a recursion with itself and simplifies it while keeping all unfolded rules. Each unfolding doubles the number of recursive steps covered. This reduces the number of…

We introduce a proof system for Hajek's logic BL based on a relational hypersequents framework. We prove that the rules of our logical calculus, called RHBL, are sound and invertible with respect to any valuation of BL into a suitable…

We first present our view of detection and correction of syntactic errors. We then introduce a new correction method, based on heuristic criteria used to decide which correction should be preferred. Weighting of these criteria leads to a…

We propose a new cyclic proof system for automated, equational reasoning about the behaviour of pure functional programs. The key to the system is the way in which cyclic proof and equational reasoning are mediated by the use of contextual…

Runtime repeated recursion unfolding was recently introduced as a just-in-time program transformation strategy that can achieve super-linear speedup. So far, the method was restricted to single linear direct recursive rules in the…

A proof tableau of Hoare logic is an annotated program with pre- and post-conditions, which corresponds to an inference tree of Hoare logic. In this paper, we show that a proof tableau for partial correctness can be transformed into an…

Suffix trees are key and efficient data structure for solving string problems. A suffix tree is a compressed trie containing all the suffixes of a given text of length $n$ with a linear construction cost. In this work, we introduce an…

Large Language Models (LLMs) are powerful candidates for complex decision-making, leveraging vast encoded knowledge and remarkable zero-shot abilities. However, their adoption in high-stakes environments is hindered by their opacity; their…

Turing machines define polynomial time (PTime) on strings but cannot deal with structures like graphs directly, and there is no known, easily computable string encoding of isomorphism classes of structures. Is there a computation model…

We present a sequent calculus system for a modal reformulation of a system of nonmonotonic logic due to McCain and Turner: we prove cut elimination for our system. The proof system is in general infinitary: because we can prove cut…

Bridging logical reasoning and deep learning is crucial for advanced AI systems. In this work, we present a new framework that addresses this goal by generating interpretable and verifiable logical rules through differentiable learning,…

This paper presents a novel framework for enhancing reasoning capabilities in large language models (LLMs) by leveraging iterative reasoning and feedback-driven methodologies. Building on the limitations identified in the SimpleBench…

The satisfiability problem for branching-time temporal logics like CTL*, CTL and CTL+ has important applications in program specification and verification. Their computational complexities are known: CTL* and CTL+ are complete for doubly…

Logic-based methods for explaining neural network decisions offer formal guarantees of correctness and non-redundancy, but they often suffer from high computational costs, especially for large networks. In this work, we improve the…

We generalize the validity criterion for the infinitary proof system of the multiplicative additive linear logic with fixed points. Our criterion is designed to take into account axioms and cuts. We show that it is sound and enjoys the cut…

In this paper, we introduce Linear Logic with a nondeterministic facility, which has a self-dual additive connective. In the system the proof net technology is available in a natural way. The important point is that nondeterminism in the…

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…