Related papers: On Establishing Robust Consistency in Answer Set P…
A popular approach for addressing uncertainty in variational inequality problems is by solving the expected residual minimization (ERM) problem. This avenue necessitates distributional information associated with the uncertainty and…
In this work we provide alternative formulations of the concepts of lambda theory and extensional theory without introducing the notion of substitution and the sets of all, free and bound variables occurring in a term. We also clarify the…
Many problems in nonlinear analysis and optimization, among them variational inequalities and minimization of convex functions, can be reduced to finding zeros (namely, roots) of set-valued operators. Hence numerous algorithms have been…
Multidimensional combinatorial substitutions are rules that replace symbols by finite patterns of symbols in $\mathbb Z^d$. We focus on the case where the patterns are not necessarily rectangular, which requires a specific description of…
Large language models (LLMs) can generate programs that pass unit tests, but passing tests does not guarantee reliable runtime behavior. We find that different correct solutions to the same task can show very different memory and…
In the field of constraint satisfaction problems (CSP), a clause is called redundant if its satisfaction is implied by satisfying all other clauses. An instance of CSP$(P)$ is called non-redundant if it does not contain any redundant…
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…
LLMs are increasingly used as general-purpose reasoners, but long inputs remain bottlenecked by a fixed context window. Recursive Language Models (RLMs) address this by externalising the prompt and recursively solving subproblems. Yet…
In many situations humans have to reason with inconsistent knowledge. These inconsistencies may occur due to not fully reliable sources of information. In order to reason with inconsistent knowledge, it is not possible to view a set of…
Answer Set Programming (ASP) is a well-established formalism for logic programming. Problem solving in ASP requires to write an ASP program whose answers sets correspond to solutions. Albeit the non-existence of answer sets for some ASP…
Identifying conflicting requirements is a key challenge in software requirement engineering, often overlooked in automated solutions. Most existing approaches rely on handcrafted rules or struggle to generalize across different domains. In…
In this paper, we apply incremental answer set solving to product configuration. Incremental answer set solving is a step-wise incremental approach to Answer Set Programming (ASP). We demonstrate how to use this technique to solve product…
A common solution for mitigating outdated or incorrect information in Large Language Models (LLMs) is to provide updated facts in-context or through knowledge editing. However, these methods introduce knowledge conflicts when the knowledge…
DO-178C stands out as a guiding standard for aviation system development processes. This standard not only mandates ensuring the consistency of requirements in the software verification process but also recognizes it as a mandatory element.…
As large language models (LLMs) are increasingly deployed to perform tasks with minimal human oversight, it is crucial that these models operate robustly. In particular, a model that can solve a given problem should not fail simply because…
We provide here a proof theoretic account of constraint programming that attempts to capture the essential ingredients of this programming style. We exemplify it by presenting proof rules for linear constraints over interval domains, and…
There are some recent approaches and results about the use of answer-set programming for specifying counterfactual interventions on entities under classification, and reasoning about them. These approaches are flexible and modular in that…
An algorithm for computing the stable model semantics of logic programs is developed. It is shown that one can extend the semantics and the algorithm to handle new and more expressive types of rules. Emphasis is placed on the use of…
The reliability of large language models (LLMs) is greatly compromised by their tendency to hallucinate, underscoring the need for precise identification of knowledge gaps within LLMs. Various methods for probing such gaps exist, ranging…
In this paper a new mathematical procedure is presented for combining different pieces of evidence which are represented in the interval form to reflect our knowledge about the truth of a hypothesis. Evidences may be correlated to each…