arXiv subjects

Zhenghua Pan

Publications and source records attributed to Zhenghua Pan.

5 recordsLinked to original sources

arXiv2026

Three Types of Negation of Triple and its Elements and an Extension of Triple

In various data models, the classical triple is a typical semantic data model. However, due to the design of the triple as a simple structure for representing positive assertions, it cannot sufficiently express different forms of negation present in the triple and its elements. This paper conceptually proposes that there are three distinct forms of negation within triples and their elements: contradictory negation, opposite negation and intermediary negation. Based on the the set SCOI and the logic LCOI+PLCOI with three kinds of negation, we propose an extension of triple that can distinguish and express these three different negations in the triple and its elements, called the TCOI triple with contradictory negation, opposite negation and intermediary negation. The TCOI triple is a semantic and structural extension of the classical triple. While retaining the ability to express positive assertions, it systematically introduces the three semantic dimensions of three negations, allowing these negations to independently act on the elements of the triple and on the whole triple. This significantly enhances the triple model capability to represent and reasoning about complex negative information. This paper also explores the expressive power and reasoning of the TCOI triple, as well as the application of TCOI triple implication reasoning in counterfactuals and counterfactual reasoning. We propose a truth-value (continuous value) algorithm for TCOI triple implication reasoning and perform its calculation through an example of the counterfactuals and counterfactual reasoning.

cs.AI↗

arXiv2026

Modus Tollens and Counterfactuals and Counterfactual Reasoning Based on Three Types of Negation

Modus Tollens (MT) is a classical logical inference rule, while counterfactuals are hypothetical statements that are contrary to facts, and counterfactual reasoning is a process of reasoning based on counterfactuals. Negation is an indispensable core concept in them. In this paper, based on the logical systems LCOI&PLCOI with contradictory negation, opposite negation and intermediary negation, we propose three variants of Modus Tollens corresponding to distinct negation types, namely MTC: Modus Tollens based on contradictory negation, MTO: Modus Tollens based on opposite negation, and MTI: Modus Tollens based on intermediary negation. We define the implications within MTC, MTO and MTI, provide the truth value algorithms of MTC, MTO and MTI, and discuss the reducibility of these algorithms. To incorporate these three types of negation into counterfactuals and counterfactual reasoning, we differentiate counterfactuals into two types based on whether they possess logical negation, thereby proposing three counterfactuals and counterfactuals reasoning based on different logical negations. In this paper, we further argue that the three counterfactuals reasoning based on different logical negations have the same inference form as MTC, MTO and MTI, respectively. In other words, they share the same inference structure. As a result, the truth value algorithms for MTC, MTO and MTI can be as the truth value algorithms for the three counterfactuals reasoning based on different logical negations. The algorithms indicates that if the first premise of the reasoning is true, the truth values of the reasoning conclusions are identical to the truth values of the three negative premises in the reasoning premises, respectively. This reflects the consistency and accuracy of the truth value algorithms.

cs.AI↗

arXiv2026

Formal Concept Analysis with Three Types of Negation

Classic Formal Concept Analysis (FCA) primarily focuses on the positive relationships between objects and attributes and does not have mechanisms for handling negation.To overcome this limitation, we introduce three types of negation concepts (contradictory negation, opposite negation, intermediary negation) into FCA.Based on the set SCOI and logic LCOI+PLCOI with these three types negation, we define formal context, Galois connection operators, formal concept and concept lattice with three types of negation,this leads to the proposal of a FCACOI: Formal Concept Analysis with contradictory negation, opposite negation and intermediary negation.For the reasoning in FCACOI, this paper focuses on attribute implication reasoning. Based on the logic LCOI+PLCOI and its semantics, we introduce the notion of ICOI-entailment as the semantic implication for attribute implication reasoning in FCACOI. Through ICOI-entailment, a connection is established between attribute implication reasoning in FCACOI and inference in the logic LCOI+PLCOI, it indicate that formally proven inference rules (theorems) in LCOI+PLCOI are valid in the attribute implication reasoning of FCACOI, LCOI+PLCOI provides a logical foundation for attribute implication reasoning in FCACOI. To illustrate the capability of attribute implication reasoning in FCACOI, we discuss its application in a concrete example. Moreover, we explore attribute reduction of the formal context in FCACOI, propose two research frameworks for attribute reduction from different perspectives, and compare their characteristics.We believe that, based on richer logic and semantics, FCACOI elevates FCA from a theory that describes affirmations to one that can describe affirmations and its contradiction(either this or that), opposition(extreme negation) and intermediary (transitional states between oppositions).

cs.AI↗

arXiv2026

Evaluating Time Series Foundation Models for Electricity Price Forecasting: Contamination Risk, Distributional Shifts, and Covariate Dependence

Time series foundation models (TSFMs) have shown strong zero-shot forecasting performance, but their generalization in covariate-driven, non-stationary settings is underexplored. Electricity price forecasting (EPF) presents a challenging testbed due to complex temporal dependencies, distributional shifts, and strong reliance on structural and contextual information. We propose a two-dataset-benchmarking framework for EPF to mitigate contamination risk and enable fair evaluation of TSFMs. We examine key aspects of EPF including point and probabilistic forecasting performance, tail behavior, price spikes, and comparisons against domain-specific methods. We find that TSFMs are highly competitive and often outperform general-purpose baselines. Yet, their performance depends critically on covariate support, and they do not consistently surpass domain-specific methods tailored to EPF. Interestingly, simple ensembles of TSFMs and domain-specific methods appear to have significant potential, suggesting that the two approaches capture complementary predictive information.

cs.LG↗

arXiv2025

Three Kinds of Negation in Knowledge and Their Mathematical Foundations

In the field of artificial intelligence, understanding, distinguishing, expressing, and computing the negation in knowledge is a fundamental issue in knowledge processing and research. In this paper, we examine and analyze the understanding and characteristics of negation in various fields such as philosophy, logic, and linguistics etc. Based on the distinction between the concepts of contradiction and opposition, we propose that there are three different types of negation in knowledge from a conceptual perspective: contradictory negation, opposite negation, and intermediary negation. To establish a mathematical foundation that fully reflects the intrinsic connections, properties, and laws of these different forms of negation, we introduce SCOI: sets with contradictory negation, opposite negation and intermediary negation, and LCOI: logic with contradictory negation, opposite negation and intermediary negation, and we proved the main operational properties of SCOI as well as the formal inference relations in LCOI.

cs.AI↗