LINC: A Neurosymbolic Approach for Logical Reasoning by Combining Language Models with First-Order Logic Provers

Logical reasoning, i.e., deductively inferring the truth value of a conclusion from a set of premises, is an important task for artificial intelligence with wide potential impacts on science, mathematics, and society. While many prompting-based strategies have been proposed to enable Large Language Models (LLMs) to do such reasoning more effectively, they still appear unsatisfactory, often failing in subtle and unpredictable ways. In this work, we investigate the validity of instead reformulating such tasks as modular neurosymbolic programming, which we call LINC: Logical Inference via Neurosymbolic Computation. In LINC, the LLM acts as a semantic parser, translating premises and conclusions from natural language to expressions in first-order logic. These expressions are then offloaded to an external theorem prover, which symbolically performs deductive inference. Leveraging this approach, we observe significant performance gains on FOLIO and a balanced subset of ProofWriter for three different models in nearly all experimental conditions we evaluate. On ProofWriter, augmenting the comparatively small open-source StarCoder+ (15.5B parameters) with LINC even outperforms GPT-3.5 and GPT-4 with Chain-of-Thought (CoT) prompting by an absolute 38% and 10%, respectively. When used with GPT-4, LINC scores 26% higher than CoT on ProofWriter while performing comparatively on FOLIO. Further analysis reveals that although both methods on average succeed roughly equally often on this dataset, they exhibit distinct and complementary failure modes. We thus provide promising evidence for how logical reasoning over natural language can be tackled through jointly leveraging LLMs alongside symbolic provers. All corresponding code is publicly available at https://github.com/benlipkin/lin

Tactile thresholds are preserved yet complex sensory function is impaired over the lumbar spine of chronic non-specific low back pain patients. A preliminary investigation

Objectives: To investigate impairments in sensory function in chronic non-specific low back pain patients and the relationship between any impairment and the clinical features of the condition. Design: A cross-sectional case-control study. Setting: Laboratory based study. Participants: Nineteen chronic non-specific low back pain patients and nineteen healthy controls. Main Outcome measures: Tactile threshold, two point discrimination distance and accuracy at a task involving recognizing letters drawn over the skin of the lower back (graphaesthesia) were assessed over the lumbar spine in both groups. Pain duration, pain intensity, physical function, anxiety and depression were assessed by questionnaire in the back pain group Results: We found no difference in tactile threshold between the two groups (median difference 0.00 95% CI -0.04 – 0.04). There was a significant difference between controls and back pain patients for two point discrimination (mean difference 17.85 95% CI 5.93 – 29.77) and graphaesthesia accuracy (mean difference 6.13 95% CI 1.27-10.99). Low back pain patients had a larger lumbar two point discrimination distance threshold and a greater letter recognition error rate. In the patient group, we found no relationship between clinical profile and sensory function and no relationship between the sensory tests. Conclusions: These data support existing findings of perceptual abnormalities in chronic non-specific low back pain patients and are suggestive of cortical rather than peripheral sensory dysfunction. Amelioration of these abnormalities may present a target for therapeutic intervention

Rayleigh superradiance and dynamic Bragg gratings in an end-pumped Bose-Einstein condensate

We study experimentally superradiant Rayleigh scattering from a Bose-Einstein condensate (BEC) in a new parameter regime where pump depletion and the exchange of photons between the endfire modes are important. Through experiments and simulations we show that collective atom light coupling leads to the self-organized formation of dynamic Bragg gratings within the sample. These gratings lead to an efficient back-scattering of pump photons and optical resonator structures within the BEC.Comment: 5 pages, 3 figure

Investigation of Phase-Lagged Boundary Conditions for Turbulence Resolving Turbomachinery Simulations

The present work explores whether phase-lagged boundary conditions can be used to perform scale resolving simulations of turbomachines. The phase-lagged approach considered is based on storing the flow signal, both at the pitch-wise boundaries and the rotor-stator interface, as its temporal Fourier coefficients for a finite number of harmonics. The method is implemented in an in-house CFD solver, G3D::Flow, which can perform both URANS and hybrid RANS/LES simulations. In order to evaluate the performance of the phase-lagged boundary condition, a comparison is made with a sliding mesh simulation on a compressor cascade. Furthermore, the possibility of breaking an error feedback loop generated in the sampling process by including multiple blade passages is also investigated. It is found that this approach greatly improves convergence and accuracy of the sampling

Haptic pop-out of movable stimuli

When, in visual and haptic search, a target is easily found among distractors, this is called a pop-out effect. The target feature is then believed to be salient, and the search is performed in a parallel way. We investigated this effect with movable stimuli in a haptic search task. The task was to find a movable ball among anchored distractors or the other way round. Results show that reaction times were independent of the number of distractors if the movable ball was the target but increased with the number of items if the anchored ball was the target. Analysis of hand movements revealed a parallel search strategy, shorter movement paths, a higher average movement speed, and a narrower direction distribution with the movable target, as compared with a more detailed search for an anchored target. Taken together, these results show that a movable object pops out between anchored objects and this indicates that movability is a salient object feature. Vibratory signals resulting from the movable ball were found to be a reasonable explanation regarding the sensation responsible for the pop-out of movability

A common neural scale for the subjective pleasantness of different primary rewards.

When an economic decision is taken, it is between goals with different values, and the values must be on the same scale. Here, we used functional MRI to search for a brain region that represents the subjective pleasantness of two different rewards on the same neural scale. We found activity in the ventral prefrontal cortex that correlated with the subjective pleasantness of two fundamentally different rewards, taste in the mouth and warmth on the hand. The evidence came from two different investigations, a between-group comparison of two independent fMRI studies, and from a within-subject study. In the latter, we showed that neural activity in the same voxels in the ventral prefrontal cortex correlated with the subjective pleasantness of the different rewards. Moreover, the slope and intercept for the regression lines describing the relationship between activations and subjective pleasantness were highly similar for the different rewards. We also provide evidence that the activations did not simply represent multisensory integration or the salience of the rewards. The findings demonstrate the existence of a specific region in the human brain where neural activity scales with the subjective pleasantness of qualitatively different primary rewards. This suggests a principle of brain processing of importance in reward valuation and decision-making

The cellular and synaptic architecture of the mechanosensory dorsal horn

The deep dorsal horn is a poorly characterized spinal cord region implicated in processing low-threshold mechanoreceptor (LTMR) information. We report an array of mouse genetic tools for defining neuronal components and functions of the dorsal horn LTMR-recipient zone (LTMR-RZ), a role for LTMR-RZ processing in tactile perception, and the basic logic of LTMR-RZ organization. We found an unexpectedly high degree of neuronal diversity in the LTMR-RZ: seven excitatory and four inhibitory subtypes of interneurons exhibiting unique morphological, physiological, and synaptic properties. Remarkably, LTMRs form synapses on between four and 11 LTMR-RZ interneuron subtypes, while each LTMR-RZ interneuron subtype samples inputs from at least one to three LTMR classes, as well as spinal cord interneurons and corticospinal neurons. Thus, the LTMR-RZ is a somatosensory processing region endowed with a neuronal complexity that rivals the retina and functions to pattern the activity of ascending touch pathways that underlie tactile perception

The involvement of tau in nucleolar transcription and the stress response

Tau is known for its pathological role in neurodegenerative diseases, including Alzheimer’s disease (AD) and other tauopathies. Tau is found in many subcellular compartments such as the cytosol and the nucleus. Although its normal role in microtubule binding is well established, its nuclear role is still unclear. Here, we reveal that tau localises to the nucleolus in undifferentiated and differentiated neuroblastoma cells (SHSY5Y), where it associates with TIP5, a key player in heterochromatin stability and ribosomal DNA (rDNA) transcriptional repression. Immunogold labelling on human brain sample confirms the physiological relevance of this finding by showing tau within the nucleolus colocalises with TIP5. Depletion of tau results in an increase in rDNA transcription with an associated decrease in heterochromatin and DNA methylation, suggesting that under normal conditions tau is involved in silencing of the rDNA. Cellular stress induced by glutamate causes nucleolar stress associated with the redistribution of nucleolar non-phosphorylated tau, in a similar manner to fibrillarin, and nuclear upsurge of phosphorylated tau (Thr231) which doesn’t colocalise with fibrillarin or nucleolar tau. This suggests that stress may impact on different nuclear tau species. In addition to involvement in rDNA transcription, nucleolar non-phosphorylated tau also undergoes stress-induced redistribution similar to many nucleolar protein