Related papers: On the comprehension schema in LP=>
We augment LP with a strong conditional operator, to yield a logic we call "strong LP," or LP=>. The resulting logic can speak of consistency in more discriminating ways, but introduces new possibilities for trivializing paradoxes.
We treat interpolation for various logics.
Despite the great potential of large language models(LLMs) in machine comprehension, it is still disturbing to fully count on them in real-world scenarios. This is probably because there is no rational explanation for whether the…
Despite significant progress in natural language understanding, Large Language Models (LLMs) remain error-prone when performing logical reasoning, often lacking the robust mental representations that enable human-like comprehension. We…
We develop a semantics for logics of imperfect information with respect to general models. Then we build a proof system and prove its soundness and completeness with respect to this semantics.
This paper describes a system, called PLP, for compiling ordered logic programs into standard logic programs under the answer set semantics. In an ordered logic program, rules are named by unique terms, and preferences among rules are given…
In this introductory article we present the basics of an approach to implementing computational interpreting of natural language aiming to model the meanings of words and phrases. Unlike other approaches, we attempt to define the meanings…
We develop first-order logic and some extensions for incomplete information scenarios and consider related complexity issues.
The topic of comprehensibility of machine-learned theories has recently drawn increasing attention. Inductive Logic Programming (ILP) uses logic programming to derive logic theories from small data based on abduction and induction…
Machine Learning has been successfully applied in systems applications such as memory prefetching and caching, where learned models have been shown to outperform heuristics. However, the lack of understanding the inner workings of these…
Subset models provide a new semantics for justifcation logic. The main idea of subset models is that evidence terms are interpreted as sets of possible worlds. A term then justifies a formula if that formula is true in each world of the…
Deep learning has advanced NLP, but interpretability remains limited, especially in healthcare and finance. Concept bottleneck models tie predictions to human concepts in vision, but NLP versions either use binary activations that harm text…
Machine comprehension plays an essential role in NLP and has been widely explored with dataset like MCTest. However, this dataset is too simple and too small for learning true reasoning abilities. \cite{hermann2015teaching} therefore…
The logics of knowledge are modal logics that have been shown to be effective in representing and reasoning about knowledge in multi-agent domains. Relatively few computational frameworks for dealing with computation of models and useful…
The goal of inductive logic programming is to induce a logic program (a set of logical rules) that generalises training examples. Inducing programs with many rules and literals is a major challenge. To tackle this challenge, we introduce an…
A framework is presented for a computational theory of probabilistic argument. The Probabilistic Reasoning Environment encodes knowledge at three levels. At the deepest level are a set of schemata encoding the system's domain knowledge.…
We define a model for linear logic based on two well-known ingredients: games and simulations. This model is interesting in the following respect: while it is obvious that the objects interpreting formulas are games and that everything is…
A semantical embedding of input/output logic in classical higher-order logic is presented. This embedding enables the mechanisation and automation of reasoning tasks in input/output logic with off-the-shelf higher-order theorem provers and…
We refine a model for linear logic based on two well-known ingredients: games and simulations. We have already shown that usual simulation relations form a sound notion of morphism between games; and that we can interpret all linear logic…
Concepts play a pivotal role in various human cognitive functions, including learning, reasoning and communication. However, there is very little work on endowing machines with the ability to form and reason with concepts. In particular,…