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Writing accurate numerical software is hard because of many sources of unavoidable uncertainties, including finite numerical precision of implementations. We present a programming model where the user writes a program in a real-valued…
We present an automated reasoning framework for synthesizing recursion-free programs using saturation-based theorem proving. Given a functional specification encoded as a first-order logical formula, we use a first-order theorem prover to…
Reinforcement Learning (RL) has gained significant attention across various domains. However, the increasing complexity of RL programs presents testing challenges, particularly the oracle problem: defining the correctness of the RL program.…
Over the last two decades, propositional satisfiability (SAT) has become one of the most successful and widely applied techniques for the solution of NP-complete problems. The aim of this paper is to investigate theoretically how Sat can be…
Formalisms based on temporal logics interpreted over finite strict linear orders, known in the literature as finite traces, have been used for temporal specification in automated planning, process modelling, (runtime) verification and…
The large and still increasing popularity of deep learning clashes with a major limit of neural network architectures, that consists in their lack of capability in providing human-understandable motivations of their decisions. In situations…
Large Language Models (LLMs) have revolutionized natural language processing, yet they struggle with inconsistent reasoning, particularly in novel domains and complex logical sequences. This research introduces Proof of Thought, a framework…
First-order logic (FOL) reasoning, which involves sequential deduction, is pivotal for intelligent systems and serves as a valuable task for evaluating reasoning capabilities, particularly in chain-of-thought (CoT) contexts. Existing…
Large language models (LLMs) have achieved remarkable performance on a variety of natural language understanding tasks. However, existing benchmarks are inadequate in measuring the complex logical reasoning capabilities of a model. We…
The use of formal language for deductive logical reasoning aligns well with language models (LMs), where translating natural language (NL) into first-order logic (FOL) and employing an external solver results in a verifiable and therefore…
Expressing program correctness often requires relating program data throughout (different branches of) an execution. Such properties can be represented using CTL+FO, a logic that allows mixing temporal and first-order quantification.…
Fault localization is a critical process that involves identifying specific program elements responsible for program failures. Manually pinpointing these elements, such as classes, methods, or statements, which are associated with a fault…
Modal logic S5 has attracted significant attention and has led to several practical applications, owing to its simplified approach to dealing with nesting modal operators. Efficient implementations for evaluating satisfiability of S5…
Satisfiability Modulo Theories (SMT) refers to the problem of deciding the satisfiability of a formula with respect to certain background first order theories. In this paper, we focus on Satisfiablity Modulo Integer Arithmetic, which is…
The recent successful paradigm of solving logical reasoning problems with tool-augmented large language models (LLMs) leverages translation of natural language (NL) statements into First-Order Logic~(FOL) and external theorem provers.…
Large Language Models (LLMs) excel at understanding natural language but struggle with optimisation tasks involving multiple constraints and user-defined preferences, which commonly arise in domains such as robotics. We propose a hybrid…
In solving a query, the SLD proof procedure for definite programs sometimes searches an infinite space for a non existing solution. For example, querying a planner for an unreachable goal state. Such programs motivate the development of…
We consider the two-variable fragment of first-order logic with one distinguished binary predicate constrained to be interpreted as a transitive relation. The finite satisfiability problem for this logic is shown to be decidable, in triply…
While a number of weak consistency mechanisms have been developed in recent years to improve performance and ensure availability in distributed, replicated systems, ensuring correctness of transactional applications running on top of such…
In this paper, we discussed CNF-SAT problem (NP-Complete problem) and analysis two solutions that can solve the problem, the PL-Resolution algorithm and the WalkSAT algorithm. PL-Resolution is a sound and complete algorithm that can be used…