Related papers: A Resolution Prover for Coalition Logic
Coalition logic is one of the most popular logics for multi-agent systems. While epistemic extensions of coalition logic have received much attention, existence of their complete axiomatisations has so far been an open problem. In this…
A term calculus for the proofs in multiplicative-additive linear logic is introduced and motivated as a programming language for channel based concurrency. The term calculus is proved complete for a semantics in linearly distributive…
Statutory law retrieval is a typical problem in legal language processing, that has various practical applications in law engineering. Modern deep learning-based retrieval methods have achieved significant results for this problem. However,…
In this paper, we deal with a calculus system SLCD (Syllogistic Logic with Carroll Diagrams), which gives a formal approach to logical reasoning with diagrams, for representations of the fundamental Aristotelian categorical propositions and…
In this paper, we introduce a system called GamePad that can be used to explore the application of machine learning methods to theorem proving in the Coq proof assistant. Interactive theorem provers such as Coq enable users to construct…
Inconsistencies are ubiquitous in law, administration, and jurisprudence. Though a cure is too much to hope for, we propose a technological remedy. Large language models (LLMs) can accurately extract propositions from arguments and compile…
We present a tableau calculus for reasoning in fragments of natural language. We focus on the problem of pronoun resolution and the way in which it complicates automated theorem proving for natural language processing. A method for…
We present new algorithm for computing the union and intersection of all justifications for a given ontological consequence without first computing the set of all justifications. Through an empirical evaluation, we show that our approach…
Dynamic epistemic logics which model abilities of agents to make various announcements and influence each other's knowledge have been studied extensively in recent years. Two notable examples of such logics are Group Announcement Logic and…
Whereas proof assistants based on Higher-Order Logic benefit from external solvers' automation, those based on Type Theory resist automation and thus require more expertise. Indeed, the latter use a more expressive logic which is further…
This paper presents a Prolog-based reasoning module to generate counterfactual explanations given the predictions computed by a black-box classifier. The proposed symbolic reasoning module can also resolve what-if queries using the…
Rationalization, a data-centric framework, aims to build self-explanatory models to explain the prediction outcome by generating a subset of human-intelligible pieces of the input data. It involves a cooperative game model where a generator…
We propose a conjugate logic that can capture the behavior of quantum and quantum-like systems. The proposal is similar to the more generic concept of epistemic logic: it encodes knowledge or perhaps more correctly, predictions about…
The logic embedding tool provides a procedural encoding for non-classical reasoning problems into classical higher-order logic. It is extensible and can support an increasing number of different non-classical logics as reasoning targets.…
Large language models (LLMs) have been used to generate formal proofs of mathematical theorems in proofs assistants such as Lean. However, we often want to optimize a formal proof with respect to various criteria, depending on its…
Equilibrium logic is an approach to nonmonotonic reasoning that extends the stable-model and answer-set semantics for logic programs. In particular, it includes the general case of nested logic programs, where arbitrary Boolean combinations…
We introduce a new theorem prover for classical higher-order logic named auto2. The prover is designed to make use of human-specified heuristics when searching for proofs. The core algorithm is a best-first search through the space of…
Logical reasoning is a fundamental aspect of human intelligence and a key component of tasks like problem-solving and decision-making. Recent advancements have enabled Large Language Models (LLMs) to potentially exhibit reasoning…
Recent advancements in large language models (LLMs) have shown remarkable progress, yet their ability to solve complex problems remains limited. In this work, we introduce Cumulative Reasoning (CR), a structured framework that enhances LLM…
Machine-learning methods are gradually being adopted in a wide variety of social, economic, and scientific contexts, yet they are notorious for struggling with exact mathematics. A typical example is computer algebra, which includes tasks…