Sandra -- A Neuro-Symbolic Reasoner Based On Descriptions And Situations

TL;DR

Sandra introduces a differentiable, probabilistic formalization of the Description and Situation (DnS) ontology to enable perspective-based reasoning. By mapping descriptions and situations into a jointly constructed vector space and tying satisfiability to subspace membership, it yields a differentiable, neuro-symbolic layer denoted $d\mathds{P}$-Sandra that can be integrated into arbitrary neural nets. The approach achieves competitive results on I-RAVEN visual reasoning and Domain Generalization (Rotated-FashionMNIST) while adding interpretability through inferred descriptions and controllable vector-space structure. This work provides a practical pathway to combine deductive reasoning with neural representations, with potential impact on robotics, medicine, and law where partial information and multiple interpretations matter.

Abstract

This paper presents sandra, a neuro-symbolic reasoner combining vectorial representations with deductive reasoning. Sandra builds a vector space constrained by an ontology and performs reasoning over it. The geometric nature of the reasoner allows its combination with neural networks, bridging the gap with symbolic knowledge representations. Sandra is based on the Description and Situation (DnS) ontology design pattern, a formalization of frame semantics. Given a set of facts (a situation) it allows to infer all possible perspectives (descriptions) that can provide a plausible interpretation for it, even in presence of incomplete information. We prove that our method is correct with respect to the DnS model. We experiment with two different tasks and their standard benchmarks, demonstrating that, without increasing complexity, sandra (i) outperforms all the baselines (ii) provides interpretability in the classification process, and (iii) allows control over the vector space, which is designed a priori.

Figures (4)

• Figure 1: Example of two descriptions (Commerce buy and Contest winning) that are satisfied by a situation that involves the entities Bob, ENCOM, Laptop. The two descriptions define the same roles, hence they provide two different perspectives from which the situation can be interpreted.
• Figure 2: Examples of some descriptions and situations alongside the conversion of a situation into $V$ to detect the satisfied descriptions. The process of deducing which descriptions are satisfied by $\bm{f}_s$ is shown on the right.
• Figure 3: Example of two images and the descriptions they satisfy. The first image has a high probability of satisfying the FootWear description, which is reasonable considering the target label. In the second image, we can understand that the wrong classification is associated with the similar probability given to the LowerBodyClothes and UpperBodyClothes descriptions, leading to an unreliable result.
• Figure 4: Raven Progressive Matrix example. The RPM is composed by $9$ numbered Panels ($3 \times 3$), the last one will be determined based on the $8$ explicit panels. Each Panel can include a variable number of Figures with some Shape, Rotation Angle, Color, and Size.

Theorems & Definitions (16)

• Definition 1
• Definition 2
• Definition 3: satisfaction
• Corollary 1
• Definition 4: near-satisfaction
• Corollary 2
• Definition 5: $\bm{f}_d$
• Theorem 1
• proof
• Definition 6: $B_d$ and $V_d$