Related papers: Two simulations about DPLL(T)

Inductive and coinductive specifications are widely used in formalizing computational systems. Such specifications have a natural rendition in logics that support fixed-point definitions. Another useful formalization device is that of…

Process rewards have been widely used in deep reinforcement learning to improve training efficiency, reduce variance, and prevent reward hacking. In LLM reasoning, existing works also explore various solutions for learning effective process…

Consequence-based reasoning can be used to construct proofs that explain entailments of description logic (DL) ontologies. In the literature, one can find multiple consequence-based calculi for reasoning in the $\mathcal{EL}$ family of DLs,…

We study Linear Temporal Logic Modulo Theories over Finite Traces (LTLfMT), a recently introduced extension of LTL over finite traces (LTLf) where propositions are replaced by first-order formulas and where first-order variables referring…

Automating the formalization of mathematical statements for theorem proving remains a major challenge for Large Language Models (LLMs). LLMs struggle to identify and utilize the prerequisite mathematical knowledge and its corresponding…

In the former article "Formal mathematical systems including a structural induction principle" we have presented a unified theory for formal mathematical systems including recursive systems closely related to formal grammars, including the…

We lift the SCL calculus for first-order logic without equality to the SCL(T) calculus for first-order logic without equality modulo a background theory. In a nutshell, the SCL(T) calculus describes a new way to guide hierarchic resolution…

We propose a novel approach for decision making problems leveraging the generalization capabilities of large language models (LLMs). Traditional methods such as expert systems, planning algorithms, and reinforcement learning often exhibit…

The rise of multi-paradigm languages challenges traditional classification methods, leading to practical software engineering issues like interoperability defects. This systematic literature review (SLR) maps the formal foundations of…

Improving Multi-modal Large Language Models (MLLMs) in the post-training stage typically relies on supervised fine-tuning (SFT) or reinforcement learning (RL), which require expensive and manually annotated multi-modal data--an ultimately…

Large language models (LLMs) have a substantial capacity for high-level analogical reasoning: reproducing patterns in linear text that occur in their training data (zero-shot evaluation) or in the provided context (few-shot in-context…

Large language models (LLMs) face significant challenges when processing complex rule systems, as they typically treat interdependent rules as unstructured textual data rather than as logically organized frameworks. This limitation results…

In this paper, we propose Probabilistic discrete-time Projection Temporal Logic (PrPTL), which extends Projection Temporal Logic (PTL) with probability. To this end, some useful formulas are derived and some logic laws are given. Further,…

Improving the reliability of large language models (LLMs) is critical for deploying them in real-world scenarios. In this paper, we propose \textbf{Deliberative Searcher}, the first framework to integrate certainty calibration with…

This paper presents the first model-checking algorithm for an expressive modal mu-calculus over timed automata, $L^{\mathit{rel}, \mathit{af}}_{\nu,\mu}$, and reports performance results for an implementation. This mu-calculus contains…

We present a formalization of modern SAT solvers and their properties in a form of abstract state transition systems. SAT solving procedures are described as transition relations over states that represent the values of the solver's global…

Let T be Goedel's system of primitive recursive functionals of finite type in the lambda formulation. We define by constructive means using recursion on nested multisets a multivalued function I from the set of terms of T into the set of…

This paper investigates the problem of inferring knowledge from data so that the inferred knowledge is interpretable and informative to humans who have prior knowledge. Given a dataset as a collection of system trajectories, we infer…

We study machine learning formulations of inductive program synthesis; given input-output examples, we try to synthesize source code that maps inputs to corresponding outputs. Our aims are to develop new machine learning approaches based on…

Large Language Models (LLMs) have been shown to achieve breakthrough performance on complex logical reasoning tasks. Nevertheless, most existing research focuses on employing formal language to guide LLMs to derive reliable reasoning paths,…