Related papers: Fuzzy Linguistic Logic Programming and its Applica…
Combining symbolic and neural approaches has gained considerable attention in the AI community, as it is often argued that the strengths and weaknesses of these approaches are complementary. One such trend in the literature are weakly…
Static program analysis is used to summarize properties over all dynamic executions. In a unifying approach based on 3-valued logic properties are either assigned a definite value or unknown. But in summarizing a set of executions, a…
We explore the implications of using fuzzy techniques (mainly those commonly used in the linguistic description/summarization of data discipline) from a natural language generation perspective. For this, we provide an extensive discussion…
We introduce Riesz Logic, whose models are abelian lattice ordered groups, which generalise Riesz spaces (vector lattices), and show soundness and completeness. Our motivation is to provide a logic for distributional semantics of natural…
A major aspect of human reasoning involves the use of approximations. Particularly in situations where the decision-making process is under stringent time constraints, decisions are based largely on approximate, qualitative assessments of…
We propose Logic Tensor Networks: a uniform framework for integrating automatic learning and reasoning. A logic formalism called Real Logic is defined on a first-order language whereby formulas have truth-value in the interval [0,1] and…
Large Language Models (LLMs) achieve strong performance in analyzing and generating text, yet they struggle with explicit, transparent, and verifiable reasoning over complex texts such as those containing debates. In particular, they lack…
Logic has pride of place in mathematics and its 20th century offshoot, computer science. Modern symbolic logic was developed, in part, as a way to provide a formal framework for mathematics: Frege, Peano, Whitehead and Russell, as well as…
We present a logic for reasoning with if-then formulas which involve constants for rational truth degrees from the unit interval. We introduce graded semantic and syntactic entailment of formulas. We prove the logic is complete in Pavelka…
Large language models (LLMs) are a promising venue for natural language understanding and generation tasks. However, current LLMs are far from reliable: they are prone to generate non-factual information and, more crucially, to contradict…
The idea of using unfolding as a way of computing a program semantics has been applied successfully to logic programs and has shown itself a powerful tool that provides concrete, implementable results, as its outcome is actually source…
The article discusses some applications of fuzzy logic ideas to formalizing of the Case-Based Reasoning (CBR) process and to measuring the effectiveness of CBR systems
Relational properties arise in many settings: relating two versions of a program that use different data representations, noninterference properties for security, etc. The main ingredient of relational verification, relating aligned pairs…
One of the most important objectives of software engineering community has been the increase of useful models that beneficially explain the development of life cycle and precisely calculate the effort of software cost estimation. In analogy…
One of the main challenges in the area of Neuro-Symbolic AI is to perform logical reasoning in the presence of both neural and symbolic data. This requires combining heterogeneous data sources such as knowledge graphs, neural model…
The paper introduces a knowledge representation language that combines the event calculus with description logic in a logic programming framework. The purpose is to provide the user with an expressive language for modelling and analysing…
We introduce DeepProbLog, a neural probabilistic logic programming language that incorporates deep learning by means of neural predicates. We show how existing inference and learning techniques of the underlying probabilistic logic…
Prioritized default reasoning has illustrated its rich expressiveness and flexibility in knowledge representation and reasoning. However, many important aspects of prioritized default reasoning have yet to be thoroughly explored. In this…
The first contribution of this paper is the presentation of a Pavelka - like formulation of possibilistic logic in which the language is naturally enriched by two connectives which represent negation (eg) and a new type of conjunction…
We use princiles of fuzzy logic to develop a general model representing several processes in a system's operation characterized by a degree of vagueness and/or uncertainy. Further, we introduce three altenative measures of a fuzzy system's…