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$\{log\}$ is a programming language at the intersection of Constraint Logic Programming, set programming and declarative programming. But $\{log\}$ is also a satisfiability solver for a theory of finite sets and finite binary relations.…
Satisfiability Modulo Theories (SMT) specifications often rely on quantifiers to remain concise and declarative. However, checking the satisfiability of such specifications directly can be inefficient. A common optimization is to ground the…
We present Stratified Metric Temporal Logic (SMTL), a novel formalism for specifying and verifying properties of complex cyber-physical systems that exhibit behaviors across multiple temporal and abstraction scales. SMTL extends existing…
Prompt optimization has become crucial for enhancing the performance of large language models (LLMs) across a broad range of tasks. Although many research papers demonstrate its effectiveness, practical adoption is hindered because existing…
Synchronous model is a type of formal models for modelling and specifying reactive systems. It has a great advantage over other real-time models that its modelling paradigm supports a deterministic concurrent behaviour of systems. Various…
Datalog is a powerful yet elegant language that allows expressing recursive computation. Although Datalog evaluation has been extensively studied in the literature, so far, only loose upper bounds are known on how fast a Datalog program can…
Signal Temporal Logic (STL), has recently seen extensive development, owing to its rich expressivenes for autonomous planning and control. Nevertheless, existing verification and control synthesis methods are limited with respect to the…
The advancement of Large Language Models (LLMs) has greatly improved our ability to process complex language. However, accurately detecting logical fallacies remains a significant challenge. This study presents a novel and effective prompt…
Datalog is a popular logic programming language for deductive reasoning tasks in a wide array of applications, including business analytics, program analysis, and ontological reasoning. However, Datalog's restriction to flat facts over…
This paper studies Linear Temporal Logic over Finite Traces (LTLf) where proposition letters are replaced with first-order formulas interpreted over arbitrary theories, in the spirit of Satisfiability Modulo Theories. The resulting logic,…
Logic has proved essential for formally modeling software based systems. Such formal descriptions, frequently called specifications, have served not only as requirements documentation and formalisation, but also for providing the…
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…
We introduce an approach that aims to combine the usage of satisfiability modulo theories (SMT) solvers with the Combinatory Logic Synthesizer (CL)S framework. (CL)S is a tool for the automatic composition of software components from a…
Symbolic and logic computation systems ranging from computer algebra systems to theorem provers are finding their way into science, technology, mathematics and engineering. But such systems rely on explicitly or implicitly represented…
Symbolic control problems aim to synthesize control policies for dynamical systems under complex temporal specifications. For such problems, Signal Temporal Logic (STL) is increasingly used as the formal specification language due to its…
Structured outputs are essential for large language models (LLMs) in critical applications like agents and information extraction. Despite their capabilities, LLMs often generate outputs that deviate from predefined schemas, significantly…
We present two applications of egglog to mathematical optimization in JijModeling 2, a mathematical modeller whose internal representation is based on simply typed $\lambda$-calculus. First, we use egglog to improve $\LaTeX$ output for…
The ability to generate test data is often a necessary prerequisite for automated software testing. For the generated data to be fit for its intended purpose, the data usually has to satisfy various logical constraints. When testing is…
Table reasoning with large language models (LLMs) plays a critical role in building intelligent systems capable of understanding and analyzing tabular data. Despite recent progress, existing methods still face key limitations: their…
We present a novel automata-based approach to address linear temporal logic modulo theory (LTL-MT) as a specification language for data words. LTL-MT extends LTL_f by replacing atomic propositions with quantifier-free multi-sorted…