Related papers: Fuzzy Linguistic Logic Programming and its Applica…
Fuzzy Description Logics (DLs) provide a means for representing vague knowledge about an application domain. In this paper, we study fuzzy extensions of conjunctive queries (CQs) over the DL $\mathcal{SROIQ}$ based on finite chains of…
The paper aims to develop a framework for coalgebraic fuzzy geometric logic by adding modalities to the language of fuzzy geometric logic. Using the methods of coalgebra, the modal operators are introduced in the language of fuzzy geometric…
We look at the problem of revising fuzzy belief bases, i.e., belief base revision in which both formulas in the base as well as revision-input formulas can come attached with varying truth-degrees. Working within a very general framework…
Many researchers want to unify probability and logic by defining logical probability or probabilistic logic reasonably. This paper tries to unify statistics and logic so that we can use both statistical probability and logical probability…
In recent years answer set programming has been extended to deal with multi-valued predicates. The resulting formalisms allows for the modeling of continuous problems as elegantly as ASP allows for the modeling of discrete problems, by…
WordNet-like Lexical Databases (WLDs) group English words into sets of synonyms called "synsets." Although the standard WLDs are being used in many successful Text-Mining applications, they have the limitation that word-senses are…
Non deterministic applications arise in many domains, including, stochastic optimization, multi-objectives optimization, stochastic planning, contingent stochastic planning, reinforcement learning, reinforcement learning in partially…
Current intent classification approaches assign binary intent class memberships to natural language utterances while disregarding the inherent vagueness in language and the corresponding vagueness in intent class boundaries. In this work,…
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,…
Unifying probabilistic and logical learning is a key challenge in AI. We introduce a Bayesian inductive logic programming approach that learns minimum message length hypotheses from noisy data. Our approach balances hypothesis complexity…
Natural language inference (NLI) aims to determine the logical relationship between two sentences, such as Entailment, Contradiction, and Neutral. In recent years, deep learning models have become a prevailing approach to NLI, but they lack…
This paper describes a simpler way for programmers to reason about the correctness of their code. The study of semantics of logic programs has shown strong links between the model theoretic semantics (truth and falsity of atoms in the…
In psycholinguistics, the creation of controlled materials is crucial to ensure that research outcomes are solely attributed to the intended manipulations and not influenced by extraneous factors. To achieve this, psycholinguists typically…
With the increasing interest in using large language models (LLMs) for planning in natural language, understanding their behaviors becomes an important research question. This work conducts a systematic investigation of LLMs' ability to…
Probabilistic logic reasoning is a central component of such cognitive architectures as OpenCog. However, as an integrative architecture, OpenCog facilitates cognitive synergy via hybridization of different inference methods. In this paper,…
In the framework of propositional {\L}ukasiewicz logic, a suitable notion of implicit definability, tailored to the intended real-valued semantics and referring to the elements of its domain, is introduced. Several variants of implicitly…
Large Language Models (LLMs) show remarkable capabilities, yet their stochastic next-token prediction creates logical inconsistencies and reward hacking that formal symbolic systems avoid. To bridge this gap, we introduce a formal logic…
The unification of logic and probability is a long-standing concern in AI, and more generally, in the philosophy of science. In essence, logic provides an easy way to specify properties that must hold in every possible world, and…
The arrangement of things in n-dimensional space is specified as Spatial. Spatial data consists of values that denote the location and shape of objects and areas on the earths surface. Spatial information includes facts such as location of…
A multitude of different probabilistic programming languages exists today, all extending a traditional programming language with primitives to support modeling of complex, structured probability distributions. Each of these languages…