Related papers: Towards a Decidable LogicWeb via Length-Bounded De…
Online learning is the process of answering a sequence of questions based on the correct answers to the previous questions. It is studied in many research areas such as game theory, information theory and machine learning. There are two…
A logic programming paradigm which expresses solutions to problems as stable models has recently been promoted as a declarative approach to solving various combinatorial and search problems, including planning problems. In this paradigm,…
We present a novel definition of an algorithm and its corresponding algorithm language called CoLweb. The merit of CoLweb [1] is that it makes algorithm design so versatile. That is, it forces us to a high-level, proof-carrying,…
Many logic programming based approaches can be used to describe and solve combinatorial search problems. On the one hand there are definite programs and constraint logic programs that compute a solution as an answer substitution to a query…
The longitudinal evaluation of retrieval systems aims to capture how information needs and documents evolve over time. However, classical Cranfield-style retrieval evaluations only consist of a static set of queries and documents and…
A default theory can be characterized by its sets of plausible conclusions, called its extensions. But, due to the theoretical complexity of Default Logic (Sigma_2p-complete), the problem of finding such an extension is very difficult if…
Structured reasoning can improve the inference performance of large language models (LLMs), but it also introduces computational cost and control constraints. When additional reasoning structure helps, and when it instead reduces efficiency…
Although conventional logical systems based on logical calculi have been successfully used in mathematics and beyond, they have definite limitations that restrict their application in many cases. For instance, the principal condition for…
Treating syntactic equality as a logical connective -- governed by left- and right-introduction rules within the sequent calculus -- offers an elegant and powerful approach to term identity. This treatment of equality allows for the…
The ability of Large Language Models (LLMs) to perform reasoning tasks such as deduction has been widely investigated in recent years. Yet, their capacity to generate proofs-faithful, human-readable explanations of why conclusions…
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…
In this paper we propose that a restricted version of logical inference can be implemented with self-attention networks. We are aiming at showing that LLMs (Large Language Models) constructed with transformer networks can make logical…
Large language models (LLMs) have demonstrated impressive capabilities in natural language understanding and generation, including multi-step reasoning such as mathematical proving. However, existing approaches often lack an explicit and…
Among the various forms of reasoning studied in the context of artificial intelligence, qualitative reasoning makes it possible to infer new knowledge in the context of imprecise, incomplete information without numerical values. In this…
Logical formalisms provide a natural and concise means for specifying and reasoning about preferences. In this paper, we propose lexicographic logic, an extension of classical propositional logic that can express a variety of preferences,…
Traditional symbolic reasoning engines, while attractive for their precision and explicability, have a few major drawbacks: the use of brittle inference procedures that rely on exact matching (unification) of logical terms, an inability to…
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…
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.…
We present initial limit Datalog, a new extensible class of constrained Horn clauses for which the satisfiability problem is decidable. The class may be viewed as a generalisation to higher-order logic (with a simple restriction on types)…
The vast quantity of data generated and captured every day has led to a pressing need for tools and processes to organize, analyze and interrelate this data. Automated reasoning and optimization tools with inherent support for data could…