Solving Algebraic Problems with Geometry Diagrams Using Syntax-Semantics Diagram Understanding

Solving Algebraic Problems with Geometry Diagrams(APGDs)poses a significant challenge in artificial intelligence due to the complex and diverse geometric relations among geometric objects.Problems typically involve both textual descriptions and geometry diagrams,requiring a joint understanding of these modalities.Although considerable progress has been made in solving math word problems,research on solving APGDs still cannot discover implicit geometry knowledge for solving APGDs,which limits their ability to effectively solve problems.In this study,a systematic and modular three-phase scheme is proposed to design an algorithm for solving APGDs that involve textual and diagrammatic information.The three-phase scheme begins with the application of the statetransformer paradigm,modeling the problem-solving process and effectively representing the intermediate states and transformations during the process.Next,a generalized APGD-solving approach is introduced to effectively extract geometric knowledge from the problem’s textual descriptions and diagrams.Finally,a specific algorithm is designed focusing on diagram understanding,which utilizes the vectorized syntax-semantics model to extract basic geometric relations from the diagram.A method for generating derived relations,which are essential for solving APGDs,is also introduced.Experiments on real-world datasets,including geometry calculation problems and shaded area problems,demonstrate that the proposed diagram understanding method significantly improves problem-solving accuracy compared to methods relying solely on simple diagram parsing.

Solving Arithmetic Word Problems of Entailing Deep Implicit Relations by Qualia Syntax-Semantic Model

Solving arithmetic word problems that entail deep implicit relations is still a challenging problem.However,significant progress has been made in solving Arithmetic Word Problems(AWP)over the past six decades.This paper proposes to discover deep implicit relations by qualia inference to solve Arithmetic Word Problems entailing Deep Implicit Relations(DIR-AWP),such as entailing commonsense or subject-domain knowledge involved in the problem-solving process.This paper proposes to take three steps to solve DIR-AWPs,in which the first three steps are used to conduct the qualia inference process.The first step uses the prepared set of qualia-quantity models to identify qualia scenes from the explicit relations extracted by the Syntax-Semantic(S2)method from the given problem.The second step adds missing entities and deep implicit relations in order using the identified qualia scenes and the qualia-quantity models,respectively.The third step distills the relations for solving the given problem by pruning the spare branches of the qualia dependency graph of all the acquired relations.The research contributes to the field by presenting a comprehensive approach combining explicit and implicit knowledge to enhance reasoning abilities.The experimental results on Math23K demonstrate hat the proposed algorithm is superior to the baseline algorithms in solving AWPs requiring deep implicit relations.

The Descriptivist vs. Anti-descriptivist Semantics Debate between Syntax and Semantics

In this paper, I will focus on the debate between descriptivism and anti-descriptivism theory about proper names. In the introduction, l will propose an historical reconstruction of the debate, and focus in particular on Russell and Kripke＇s treatments of proper names. Strong criticisms will be advanced against Kripke＇s hypothesis of rigid-designator and, more deafly, against the consequent distinction between the epistemic and metaphysical level that Kripke proposes to explain identity assertions between proper names. Furthermore, I will argue, that, pace Kripke, Russellian treatment of proper names allows to capture all our semantic intuitions, and also those semantic interpretations which concern context-belief sentences. I will close the introduction by focusing on a criticism that Kripke rightly points out against an example that Russell proposes in his On Denoting. Section 2 will be devoted to Russellian solution： I will show that not only Russell＇s logical treatment of proper names allows to answer to Kripke＇s criticism to Russell＇s example, but also that such treatment can disambiguate and express all our semantic intuitions about Frege＇s puzzle sentence ＂Hesperus is Phosphorus.＂ ! will then show that, contrarily, Quinian solution （discussed in section 3） and Kripkian one （see section 4） are not satisfactory to capture our semantic knowledge about Frege＇s sentence. Furthermore, in section 5, I will focus on Kripke＇s distinction between epistemic and metaphysical level to deal with identity assertions between proper names, and I will logically show that such distinction is not plausible. In section 5, then, I will show that Russellian solution allows to explain context-belief sentences, contrarily to what Kripke thinks. In Conclusions, I will summarize what 1 have argued in the text.