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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…
Two lines of approaches are adopted for complex reasoning with LLMs. One line of work prompts LLMs with various reasoning structures, while the structural outputs can be naturally regarded as intermediate reasoning steps. Another line of…
As modern system of systems (SoS) become increasingly adaptive and human centred, traditional architectures often struggle to support interoperability, reconfigurability, and effective human system interaction. This paper addresses these…
Defeasible logics provide several linguistic features to support the expression of defeasible knowledge. There is also a wide variety of such logics, expressing different intuitions about defeasible reasoning. However, the logics can only…
Logical frameworks provide natural and direct ways of specifying and reasoning within deductive systems. The logical framework LF and subsequent developments focus on finitary proof systems, making the formalization of circular proof…
Reasoning is a fundamental substrate for solving novel and complex problems. Deliberate efforts in learning and developing frameworks around System 2 reasoning have made great strides, yet problems of sufficient complexity remain largely…
Humans intuitively solve complex problems by flexibly shifting among reasoning modes: they plan, execute, revise intermediate goals, resolve ambiguity through associative judgment, and apply formal procedures to well-specified subproblems.…
We introduce an extension of first-order logic that comes equipped with additional predicates for reasoning about an abstract state. Sequents in the logic comprise a main formula together with pre- and postconditions in the style of Hoare…
Epistemic logic programs constitute an extension of the stable models semantics to deal with new constructs called subjective literals. Informally speaking, a subjective literal allows checking whether some regular literal is true in all…
This paper presents an extended version of the SPADE platform, which aims to empower intelligent agent systems with normative reasoning and value alignment capabilities. Normative reasoning involves evaluating social norms and their impact…
We propose a probabilistic Hoare logic aHL based on the union bound, a tool from basic probability theory. While the union bound is simple, it is an extremely common tool for analyzing randomized algorithms. In formal verification terms,…
Our goal is a modern approach to answering questions via systematic reasoning where answers are supported by human interpretable proof trees grounded in an NL corpus of authoritative facts. Such a system would help alleviate the challenges…
Multi-hop QA requires a model to connect multiple pieces of evidence scattered in a long context to answer the question. The recently proposed HotpotQA (Yang et al., 2018) dataset is comprised of questions embodying four different multi-hop…
We present the first verified implementation of a decision procedure for the quantifier-free theory of partial and linear orders. We formalise the procedure in Isabelle/HOL and provide a specification that is made executable using…
We define a general notion of transition system where states and action labels can be from arbitrary nominal sets, actions may bind names, and state predicates from an arbitrary logic define properties of states. A Hennessy-Milner logic for…
In this paper, we observe that semi-structured tabulated text is ubiquitous; understanding them requires not only comprehending the meaning of text fragments, but also implicit relationships between them. We argue that such data can prove…
Byzantine fault tolerant protocols enable state replication in the presence of crashed, malfunctioning, or actively malicious processes. Designing such protocols without the assistance of verification tools, however, is remarkably…
Rule-based reasoning over natural language input arises in domains where decisions must be auditable and justifiable: clinical protocols specify eligibility criteria in prose, evidence rules define admissibility through textual conditions,…
We describe SeCaV, a sequent calculus verifier for first-order logic in Isabelle/HOL, and the SeCaV Unshortener, an online tool that expands succinct derivations into the full SeCaV syntax. We leverage the power of Isabelle/HOL as a proof…
In this position paper, we propose a reasoning framework that can model the reasoning process underlying natural language inferences. The framework is based on the semantic tableau method, a well-studied proof system in formal logic. Like…