This work explores the consistency of small LLMs (2B-8B parameters) in answering multiple times the same question. We present a study on known, open-source LLMs responding to 10 repetitions of questions from the multiple-choice benchmarks MMLU-Redux and MedQA, considering different inference temperatures, small vs. medium models (50B-80B), finetuned vs. base models, and other parameters. We also look into the effects of requiring multi-trial answer consistency on accuracy and the trade-offs involved in deciding which model best provides both of them. To support those studies, we propose some new analytical and graphical tools. Results show that the number of questions which can be answered consistently vary considerably among models but are typically in the 50%-80% range for small models at low inference temperatures. Also, accuracy among consistent answers seems to reasonably correlate with overall accuracy. Results for medium-sized models seem to indicate much higher levels of answer consistency.

Self-consistency (Wang et al., 2023) suggests that the most consistent answer obtained through large language models (LLMs) is more likely to be correct. In this paper, we challenge this argument and propose a nuanced correction. Our observations indicate that consistent answers derived through more computation i.e. longer reasoning texts, rather than simply the most consistent answer across all outputs, are more likely to be correct. This is predominantly because we demonstrate that LLMs can autonomously produce chain-of-thought (CoT) style reasoning with no custom prompts merely while generating longer responses, which lead to consistent predictions that are more accurate. In the zero-shot setting, by sampling Mixtral-8x7B model multiple times and considering longer responses, we achieve 86% of its self-consistency performance obtained through zero-shot CoT prompting on the GSM8K and MultiArith datasets. Finally, we demonstrate that the probability of LLMs generating a longer response is quite low, highlighting the need for decoding strategies conditioned on output length.

Given a conditional sentence "P=>Q" (if P then Q) and respective facts, four different types of inferences are observed in human reasoning. Affirming the antecedent (AA) (or modus ponens) reasons Q from P; affirming the consequent (AC) reasons P from Q; denying the antecedent (DA) reasons -Q from -P; and denying the consequent (DC) (or modus tollens) reasons -P from -Q. Among them, AA and DC are logically valid, while AC and DA are logically invalid and often called logical fallacies. Nevertheless, humans often perform AC or DA as pragmatic inference in daily life. In this paper, we realize AC, DA and DC inferences in answer set programming. Eight different types of completion are introduced and their semantics are given by answer sets. We investigate formal properties and characterize human reasoning tasks in cognitive psychology. Those completions are also applied to commonsense reasoning in AI.

Consistent answers to a query from a possibly inconsistent database are answers that are simultaneously retrieved from every possible repair of the database. Repairs are consistent instances that minimally differ from the original inconsistent instance. It has been shown before that database repairs can be specified as the stable models of a disjunctive logic program. In this paper we show how to use the repair programs to transform the problem of consistent query answering into a problem of reasoning w.r.t. a theory written in second-order predicate logic. It also investigated how a first-order theory can be obtained instead by applying second-order quantifier elimination techniques.