Related papers: On the Expressibility of Stable Logic Programming
Declarative spatial reasoning denotes the ability to (declaratively) specify and solve real-world problems related to geometric and qualitative spatial representation and reasoning within standard knowledge representation and reasoning (KR)…
An instance of Max CSP is a finite collection of constraints on a set of variables, and the goal is to assign values to the variables that maximises the number of satisfied constraints. Max CSP captures many well-known problems (such as Max…
Several works have shown that perturbation stable instances of the MAP inference problem in Potts models can be solved exactly using a natural linear programming (LP) relaxation. However, most of these works give few (or no) guarantees for…
The Stable Marriage problem (SM), solved by the famous deferred acceptance algorithm of Gale and Shapley (GS), has many natural generalizations. If we allow ties in preferences, then the problem of finding a maximum stable matching becomes…
To any fixed, finite relational structure, $\mathbb{D}$, there is an associated decision problem, CSP$(\mathbb{D})$, which is a restricted version of the constraint satisfaction problem. In [8], the so called "algebraic approach" to the…
The P versus NP problem asks whether every language verifiable in polynomial time can also be decided in deterministic polynomial time. In this paper, we present a constructive proof that P = NP by introducing a universal, graph-based…
Similarity-based Logic Programming (briefly, SLP ) has been proposed to enhance the LP paradigm with a kind of approximate reasoning which supports flexible information retrieval applications. This approach uses a fuzzy similarity relation…
Logic programming (LP) is a programming language based on first-order Horn clause logic that uses SLD-resolution as a semi-decision procedure. Finite SLD-computations are inductively sound and complete with respect to least Herbrand models…
Systematic scenario generation (SG) methods have emerged as an invaluable tool to handle uncertainty towards the efficient solution of stochastic programming (SP) problems. The quality of SG methods depends on their consistency to generate…
Model counting is the problem of computing the number of models that satisfy a given propositional theory. It has recently been applied to solving inference tasks in probabilistic logic programming, where the goal is to compute the…
Motivated by the quest for a logic for PTIME and recent insights that the descriptive complexity of problems from linear algebra is a crucial aspect of this problem, we study the solvability of linear equation systems over finite groups and…
Large Language Models (LLMs) have demonstrated impressive reasoning capabilities, leading to their adoption in high-stakes domains such as healthcare, law, and scientific research. However, their reasoning often contains subtle logical…
In this paper, a fully compressed pattern matching problem is studied. The compression is represented by straight-line programs (SLPs), i.e. a context-free grammars generating exactly one string; the term fully means that both the pattern…
Recent large language models (LLMs) have achieved impressive reasoning milestones but continue to struggle with high computational costs, logical inconsistencies, and sharp performance degradation on high-complexity problems. While…
Linear and semidefinite programming (LP, SDP), regularisation through basis pursuit (BP) and Lasso have seen great success in mathematics, statistics, data science, computer-assisted proofs and learning. The success of LP is traditionally…
We introduce a concept of efficiency for which we can prove that it applies to all paddable languages, but still does not conflict with potential worst case intractability. Note that the family of paddable languages apparently includes all…
Determination of the most economic strategies for supply and transmission of electricity is a daunting computational challenge. Due to theoretical barriers, so-called NP-hardness, the amount of effort to optimize the schedule of generating…
We present a theory of parameterized dynamic logic, namely DLp, for specifying and reasoning about a rich set of program models based on their transitional behaviours. Different from most dynamic logics that deal with regular expressions or…
Prior work has combined chain-of-thought prompting in large language models (LLMs) with programmatic representations to perform effective and transparent reasoning. While such an approach works well for tasks that only require forward…
Semantic Tube Prediction (STP) leverages representation geometric to regularize LLM hidden-state trajectories toward locally linear geodesics during fine-tuning, thereby greatly improving data efficiency. The original STP recipe samples…