Related papers: A Constraint-based Mathematical Modeling Library i…
We propose utilizing background operators for mathematical reasoning in large language models (LLMs). To achieve this, we define a set of fundamental mathematical predicates as the basic building blocks. For each mathematical problem, we…
This paper presents matching logic, a first-order logic (FOL) variant for specifying and reasoning about structure by means of patterns and pattern matching. Its sentences, the patterns, are constructed using variables, symbols, connectives…
When solving combinatorial problems, pruning symmetric solution candidates from the search space is essential. Most of the existing approaches are instance-specific and focus on the automatic computation of Symmetry Breaking Constraints…
Coding standards and good practices are fundamental to a disciplined approach to software projects, whatever programming languages they employ. Prolog programming can benefit from such an approach, perhaps more than programming in other…
Large Language Models (LLMs) have demonstrated strong performance across various general Natural Language Processing (NLP) tasks. However, their effectiveness in financial credit assessment applications remains suboptimal, primarily due to…
We present initial limit Datalog, a new extensible class of constrained Horn clauses for which the satisfiability problem is decidable. The class may be viewed as a generalisation to higher-order logic (with a simple restriction on types)…
Combining a set of existing constraint solvers into an integrated system of cooperating solvers is a useful and economic principle to solve hybrid constraint problems. In this paper we show that this approach can also be used to integrate…
Constraint Answer Set Programming (CASP) is a hybrid paradigm that enriches Answer Set Programming (ASP) with numerical constraint processing, a crucial requirement for many real-world applications. However, the specification of constraints…
The dominant approach to generating from language models subject to some constraint is locally constrained decoding (LCD), incrementally sampling tokens at each time step such that the constraint is never violated. Typically, this is…
Enhancing the adaptive capabilities of large language models is a critical pursuit in both research and application. Traditional fine-tuning methods require substantial data and computational resources, especially for enhancing specific…
Logic programming is a flexible programming paradigm due to the use of predicates without a fixed data flow. To extend logic languages with the compact notation of functional programming, there are various proposals to map evaluable…
In most machine learning applications, classification accuracy is not the primary metric of interest. Binary classifiers which face class imbalance are often evaluated by the $F_\beta$ score, area under the precision-recall curve, Precision…
Large language models (LLMs) have shown promising performance across diverse domains. Many practical applications of LLMs, such as code completion and structured data extraction, require adherence to syntactic constraints specified by a…
Although unification can be used to implement a weak form of $\beta$-reduction, several linguistic phenomena are better handled by using some form of $\lambda$-calculus. In this paper we present a higher order feature description calculus…
In this paper, we characterize the properties of a direct interpretation of HPSG and present the advantages of this approach. High-level programming languages constitute in this perspective an efficient solution: we show how a…
In-context learning enables language models (LM) to adapt to downstream data or tasks by incorporating few samples as demonstrations within the prompts. It offers strong performance without the expense of fine-tuning. However, the…
Synthesizing programs using example input/outputs is a classic problem in artificial intelligence. We present a method for solving Programming By Example (PBE) problems by using a neural model to guide the search of a constraint logic…
We provide a denotational semantics for first-order logic that captures the two-level view of the computation process typical for constraint programming. At one level we have the usual program execution. At the other level an automatic…
Logic can be made useful for programming and for databases independently of logic programming. To be useful in this way, logic has to provide a mechanism for the definition of new functions and new relations on the basis of those given in…
Compared with constraint satisfaction problems, counting problems have received less attention. In this paper, we survey research works on the problems of counting the number of solutions to constraints. The constraints may take various…