CALM: Contextual Analog Logic with Multimodality

• CALM Framework is a hybrid AI reasoning system that integrates symbolic logic with multimodal neural perception to compute continuous (analog) truth values for context-sensitive tasks.
• It employs a hierarchical domain tree structure and fuzzy logic operators to replace rigid binary evaluations with graded, interpretable outcomes in spatial and semantic tasks.
• Empirical results show CALM achieves 92.2% accuracy in object placement tasks, outperforming classical logic and neural-only models while providing intuitive heatmap visualizations.

Contextual Analog Logic with Multimodality (CALM) is a hybrid AI reasoning framework that integrates symbolic logic and multimodal neural perception to enable context-sensitive, interpretable decision-making grounded in real-world data. CALM addresses fundamental limitations of classical (bivalent) logic systems, which are ill-suited to the nuanced, context-dependent decisions encountered in tasks like spatial arrangement and object placement, and of neural models, whose rich sensory representations often lack structural interpretability or robust logical guarantees. CALM replaces rigid binary predicate evaluations with continuous (“analog”) truth values, which are dynamically inferred by neural networks conditioned on multimodal inputs—such as images and text—while a symbolic reasoning engine enforces logical consistency via structured constraint search and analog connectives. This fusion allows CALM to navigate ambiguous real-world environments, offering both the precision of logic and the flexibility of learned perceptual representations (Jacobson et al., 17 Jun 2025).

1. Motivation and Limitations of Prior Systems

CALM was motivated by the inadequacy of classic first-order logic and modern neural systems when deployed in tasks requiring graded reasoning over perceptual domains. Classical logic encodes statements as strictly true or false; for example, enforcing “the microwave must be below the cupboard” leads to brittle, non-intuitive behavior in spatial tasks, as only a specific region is considered correct. By contrast, human preferences are often continuous: some locations are “more” appropriate, but there is no clear binary cutoff. On the other hand, neural networks interpret complex multimodal inputs but their outputs may violate required constraints or lack interpretability, making them unsuitable for applications where logical guarantees or user transparency is critical. CALM directly addresses these gaps by developing an analog logic framework in which predicates can return continuous values in [0, 1], and in which neural modules supply real-world context to symbolic structure.

2. Framework Structure and Computation of Analog Truth Values

CALM formalizes each predicate as a multi-level domain tree, hierarchically partitioning the relevant domain (e.g., spatial interval, semantic region). At each node, a predicate-specific neural module computes a set of k analog truth factors based on the modality-specific context (images, text, or both). These factors capture the degree to which the input satisfies the predicate in that subdomain. The overall analog truth value for a particular predicate grounding results from the product of the truth factors along the tree path traced by the chosen assignment:

$T = t_1 \cdot t_2 \cdots t_n$

where $t_i$ is the neural output at domain refinement level $i$. This approach allows the model to reflect gradations in spatial or semantic compatibility, with larger or more flexible “true” regions for predicates whose natural language analog admits fuzziness.

CALM defines logical connectives using fuzzy logic operators:

• AND ($A \land B$): $min(A, B)$
• OR ($A \lor B$): $max(A, B)$
• NOT ($\neg A$): $1 - A$

Quantifiers are similarly generalized. The universal quantifier with threshold $T$ is defined as

$$\forall_{T} x \in S, P(x) \iff \min_{x \in S} P(x) \geq T$$

This enables quantification over analog predicates, maintaining structured constraint satisfaction.

3. Integration of Symbolic and Neural Reasoning

CALM’s pipeline combines learned perception and explicit symbol manipulation in inference. For each predicate (e.g., “LeftOf”, “Below”), a neural model (often leveraging encoders such as CLIP or ResNet for images and transformers for text) analyzes the multi-modal context to output analog truth factors for all subdomains. The symbolic reasoning engine assembles these analog predicate results using generalized logical formulas (domain trees, min/max operators, analog quantification).

During inference, CALM supports three principal modes:

1. Truth Evaluation: Computes the analog truth of a specific grounding (full assignment of variables) by traversing domain trees and multiplying associated neural outputs.
2. Truth Maximization: Searches for groundings maximizing the total analog truth of the logical formula, ensuring that both constraints and soft preferences are satisfied to the greatest extent.
3. Truth-Proportional Sampling: Generates plausible groundings according to their analog truth, enabling informed sampling for applications like generative design or layout proposal.

The symbolic search is structured and backtracking-aware, ensuring that global constraints are never violated, even as the neural modules provide context-sensitive flexibility.

4. Empirical Results and Benchmark Evaluation

In a suite of fill-in-the-blank object placement tasks—tasks requiring the selection of an object position subject to ambiguous natural-language constraints—CALM achieved an object placement accuracy of 92.2%, outperforming classical logic (first-order logic with uniform sampling, 86.3%) and large pre-trained vision-LLM baselines (59.4%). CALM also demonstrated the ability to produce spatial heatmaps, where color intensity encodes analog truth, providing intuitive visualization of plausibility regions for object placement.

A human paper established that CALM-generated heatmaps are more aligned with both the provided logic and human spatial preferences than those produced by logic-only or neural-only baselines, with results significant at $p < 0.0001$. This demonstrates CALM’s ability to respect hard symbolic constraints while aligning with nuanced, multi-modal perceptual context.

5. Logical, Mathematical, and Implementation Details

CALM’s formalism relies on direct analogs to fuzzy logic operations and integrates these with neural context evaluators:

• Conjunction: $A \land B = \min(A, B)$
• Disjunction: $A \lor B = \max(A, B)$
• Negation: $\neg A = 1 - A$
• Universal quantification: $$\forall_{T} x \in S, P(x) \iff \min_{x \in S} P(x) \geq T$$
• Analog predicate value from domain trees: $T = \prod_{i=1}^n t_i$, with $t_i$ the neural output at refinement $i$.

CALM’s architecture modularizes neural predicate evaluators and symbolic constraint logic, enabling extensibility to arbitrary modalities and logic structures. The approach is illustrated in the paper via diagrams showing domain tree traversal and heatmap generation, highlighting its interpretability advantages.

6. Implications, Applications, and Future Directions

CALM’s hybrid structure enables AI systems to achieve both the interpretability and generalization required for real-world, context-sensitive reasoning. Potential applications include:

• Robotics and manipulation (e.g., instructable spatial reasoning)
• Interior design, architecture, and layout generation using logical statements and perceptual constraints
• Image editing and inpainting, where logical structure guides the placement or modification of scene elements with models such as Stable Diffusion

Its domain tree approach and analog truth values provide a path toward robust, compositional reasoning in multi-modal environments without sacrificing structural guarantees. CALM generalizes to tasks where neither symbolic nor neural approaches alone suffice.

Future research may extend CALM to broader classes of predicates, richer multi-modal input spaces, and interactive or online learning settings. Its modular design positions it as a foundational framework for next-generation AI requiring both precision and context-driven generalization (Jacobson et al., 17 Jun 2025).