Quantitative Constraint Logic Programming for Weighted Grammar Applications

We study weighted programming, a programming paradigm for specifying mathematical models. More specifically, the weighted programs we investigate are like usual imperative programs with two additional features: (1) nondeterministic branching and (2) weighting execution traces. Weights can be numbers but also other objects like words from an alphabet, polynomials, formal power series, or cardinal numbers. We argue that weighted programming as a paradigm can be used to specify ...

We present a probabilistic model for constraint-based grammars and a method for estimating the parameters of such models from incomplete, i.e., unparsed data. Whereas methods exist to estimate the parameters of probabilistic context-free grammars from incomplete data (Baum 1970), so far for probabilistic grammars involving context-dependencies only parameter estimation techniques from complete, i.e., fully parsed data have been presented (Abney 1997). However, complete-data e...

Qualitative modelling is a technique integrating the fields of theoretical computer science, artificial intelligence and the physical and biological sciences. The aim is to be able to model the behaviour of systems without estimating parameter values and fixing the exact quantitative dynamics. Traditional applications are the study of the dynamics of physical and biological systems at a higher level of abstraction than that obtained by estimation of numerical parameter values...

Weighted programs generalize probabilistic programs and offer a framework for specifying and encoding mathematical models by means of an algorithmic representation. Kleene algebra with tests is an algebraic formalism based on regular expressions with applications in proving program equivalence. We extend the language of Kleene algebra with tests so that it is sufficient to formalize reasoning about a simplified version weighted programs. We introduce relational semantics for ...

While Large Language Models (LLMs) perform exceptionally well at natural language tasks, they often struggle with precise formal reasoning and the rigorous specification of problems. We present MCP-Solver, a prototype implementation of the Model Context Protocol that demonstrates the potential for systematic integration between LLMs and constraint programming systems. Our implementation provides interfaces for the creation, editing, and validation of a constraint model. Throu...

Weighted monadic second-order logic is a weighted extension of monadic second-order logic that captures exactly the behaviour of weighted automata. Its semantics is parameterized with respect to a semiring on which the values that weighted formulas output are evaluated. Gastin and Monmege (2018) gave abstract semantics for a version of weighted monadic second-order logic to give a more general and modular proof of the equivalence of the logic with weighted automata. We focus ...

We provide a constraint based computational model of linear precedence as employed in the HPSG grammar formalism. An extended feature logic which adds a wide range of constraints involving precedence is described. A sound, complete and terminating deterministic constraint solving procedure is given. Deterministic computational model is achieved by weakening the logic such that it is sufficient for linguistic applications involving word-order.

Answer Set Programming has separately been extended with constraints, to the streaming domain, and with capabilities to reason over the quantities associated with answer sets. We propose the introduction and analysis of a general framework that incorporates all three directions of extension by exploiting the strengths of Here-and-There Logic and Weighted Logic.

The Workshops on (Constraint) Logic Programming (WLP) are the annual meeting of the German Society of Logic Programming (Gesellschaft f\"ur Logische Programmierung e.V., GLP) and bring together researchers interested in logic programming, constraint programming, answer set programming, and related areas like databases and artificial intelligence (not only from Germany). The International Workshops on Functional and (Constraint) Logic Programming (WFLP) aim at bringing toget...

We present the CIFF proof procedure for abductive logic programming with constraints, and we prove its correctness. CIFF is an extension of the IFF proof procedure for abductive logic programming, relaxing the original restrictions over variable quantification (allowedness conditions) and incorporating a constraint solver to deal with numerical constraints as in constraint logic programming. Finally, we describe the CIFF system, comparing it with state of the art abductive sy...