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Prioritized Default Logic presents an optimal solution for addressing real-world problems characterized by incomplete information and the need to establish preferences among diverse scenarios. Although it has reached great success in the…
Probabilistic programming is considered as a framework, in which basic components of cognitive architectures can be represented in unified and elegant fashion. At the same time, necessity of adopting some component of cognitive…
Modern language models (LMs) exhibit strong deductive reasoning capabilities, yet standard evaluations emphasize correctness while overlooking a key aspect of reasoning: efficiency. In real-world reasoning scenarios, much of the available…
An increasing number of scientific experiments support the view of perception as Bayesian inference, which is rooted in Helmholtz's view of perception as unconscious inference. Recent study of logic presents a view of logical reasoning as…
Inductive logic programming, or relational learning, is a powerful paradigm for machine learning or data mining. However, in order for ILP to become practically useful, the efficiency of ILP systems must improve substantially. To this end,…
The past few years have seen a surge of interest in the field of probabilistic logic learning and statistical relational learning. In this endeavor, many probabilistic logics have been developed. ProbLog is a recent probabilistic extension…
We present an exact Bayesian inference method for inferring posterior distributions encoded by probabilistic programs featuring possibly unbounded loops. Our method is built on a denotational semantics represented by probability generating…
Concept Bottleneck Models (CBMs) provide a basis for semantic abstractions within a neural network architecture. Such models have primarily been seen through the lens of interpretability so far, wherein they offer transparency by inferring…
To improve word representation learning, we propose a probabilistic prior which can be seamlessly integrated with word embedding models. Different from previous methods, word embedding is taken as a probabilistic generative model, and it…
We often desire our models to be interpretable as well as accurate. Prior work on optimizing models for interpretability has relied on easy-to-quantify proxies for interpretability, such as sparsity or the number of operations required. In…
This paper illustrates how a Prolog program, using chronological backtracking to find a solution in some search space, can be enhanced to perform intelligent backtracking. The enhancement crucially relies on the impurity of Prolog that…
Imprecise-information processing will play an indispensable role in intelligent systems, especially in the anthropomorphic intelligent systems (as intelligent robots). A new theoretical and technological system of imprecise-information…
Fuzzy quantification is a subtopic of fuzzy logic which deals with the modelling of the quantified expressions we can find in natural language. Fuzzy quantifiers have been successfully applied in several fields like fuzzy, control, fuzzy…
Understanding how Large Language Models (LLMs) perform logical reasoning internally remains a fundamental challenge. While prior mechanistic studies focus on identifying taskspecific circuits, they leave open the question of what…
Logics of limited belief aim at enabling computationally feasible reasoning in highly expressive representation languages. These languages are often dialects of first-order logic with a weaker form of logical entailment that keeps reasoning…
Linear logic programming uses provability as the basis for computation. In the operational semantics based on provability, executing the additive-conjunctive goal $G_1 \& G_2$ from a program $P$ simply terminates with a success if both…
In this paper, we present the interval neutrosophic logics which generalizes the fuzzy logic, paraconsistent logic, intuitionistic fuzzy logic and many other non-classical and non-standard logics. We will give the formal definition of…
Beginning with a simple semantics for propositions, based on counting observations, it is shown that probabilistic and fuzzy logic correspond to two different heuristic assumptions regarding the combination of propositions whose evidence…
This paper discusses the merits and demerits of crisp logic and fuzzy logic with respect to their applicability in intelligent response generation by a human being and by a robot. Intelligent systems must have the capability of taking…
A model's interpretability is essential to many practical applications such as clinical decision support systems. In this paper, a novel interpretable machine learning method is presented, which can model the relationship between input…