Related papers: Lemma Generation for Horn Clause Satisfiability: A…
Alternation of forward and backward analyses is a standard technique in abstract interpretation of programs, which is in particular useful when we wish to prove unreachability of some undesired program states. The current state-of-the-art…
We propose to study proof search from a coinductive point of view. In this paper, we consider intuitionistic logic and a focused system based on Herbelin's LJT for the implicational fragment. We introduce a variant of lambda calculus with…
Tree Regular Model Checking (TRMC) is the name of a family of techniques for analyzing infinite-state systems in which states are represented by terms, and sets of states by Tree Automata (TA). The central problem in TRMC is to decide…
We define a logic of propositional formula schemata adding to the syntax of propositional logic indexed propositions and iterated connectives ranging over intervals parameterized by arithmetic variables. The satisfiability problem is shown…
We consider constrained Horn clause solving from the more general point of view of solving formula equations. Constrained Horn clauses correspond to the subclass of Horn formula equations. We state and prove a fixed-point theorem for Horn…
We propose a hybrid-dynamic first-order logic as a formal foundation for specifying and reasoning about reconfigurable systems. As the name suggests, the formalism we develop extends (many-sorted) first-order logic with features that are…
Previous results on proving confluence for Constraint Handling Rules are extended in two ways in order to allow a larger and more realistic class of CHR programs to be considered confluent. Firstly, we introduce the relaxed notion of…
First-order logic is a natural way of expressing the properties of computation, traditionally used in various program logics for expressing the correctness properties and certificates. Subsequently, modern methods in the automated inference…
Determining whether a program terminates is a central problem in computer science. Turing's Halting Problem established termination as undecidable, showing that no algorithm can universally determine termination for all programs and inputs.…
The combination of uninterpreted function symbols and universal quantification occurs in many applications of automated reasoning, for example, due to their ability to reason about arrays. Yet the satisfiability of such formulas is, in…
A definite Horn theory is a set of n-dimensional Boolean vectors whose characteristic function is expressible as a definite Horn formula, that is, as conjunction of definite Horn clauses. The class of definite Horn theories is known to be…
We study the satisfiability problem of symbolic tree automata and decompose it into the satisfiability problem of the existential first-order theory of the input characters and the existential monadic second-order theory of the indices of…
Generative large language models (LLMs) with instruct training such as GPT-4 can follow human-provided instruction prompts and generate human-like responses to these prompts. Apart from natural language responses, they have also been found…
To mitigate hallucinations in large language models (LLMs), we propose a framework that focuses on errors induced by prompts. Our method extends a chain-style knowledge distillation approach by incorporating a programmable module that…
Linear tree constraints were introduced by Hofmann and Rodriguez in the context of amortized resource analysis for object oriented programs. More precisely, they gave a reduction from inference of resource types to constraint solving. Thus,…
Proving equivalence between functional programs is a fundamental problem in program verification, which often amounts to reasoning about algebraic data types (ADTs) and compositions of structural recursions. Modern theorem provers address…
Algorithmic meta-theorems state that problems definable in a fixed logic can be solved efficiently on structures with certain properties. An example is Courcelle's Theorem, which states that all problems expressible in monadic second-order…
Recent years have witnessed increasing interests in prompt-based learning in which models can be trained on only a few annotated instances, making them suitable in low-resource settings. When using prompt-based learning for text…
The CLP scheme uses Horn clauses and SLD resolution to generate multiple constraint satisfaction problems (CSPs). The possible CSPs include rational trees (giving Prolog) and numerical algorithms for solving linear equations and linear…
We present verification methods for logic programs with delay declarations. The verified properties are termination and freedom from errors related to built-ins. Concerning termination, we present two approaches. The first approach tries to…