Related papers: Extending and Implementing the Stable Model Semant…
Linear logic (LL) is a resource-aware, abstract logic programming language that refines both classical and intuitionistic logic. Linear logic semantics is typically presented in one of two ways: by associating each formula with the set of…
In Dung-style abstract argumentation, various semantics capture notions of acceptability of arguments. The admissibility semantics capture the notion that an argument can be consistently defended from any potential counterargument. Weak…
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…
Bialgebrae provide an abstract framework encompassing the semantics of different kinds of computational models. In this paper we propose a bialgebraic approach to the semantics of logic programming. Our methodology is to study logic…
In the logic programming paradigm, a program is defined by a set of methods, each of which can be executed when specific conditions are met during the current state of an execution. The semantics of these programs can be elegantly…
As the practical use of answer set programming (ASP) has grown with the development of efficient solvers, we expect a growing interest in extensions of ASP as their semantics stabilize and solvers supporting them mature. Epistemic…
The stable model (SM) semantics lacks the properties of existence, relevance and cumulativity. If we prospectively consider the class of conservative extensions of SM semantics (i.e., semantics that for each normal logic program P retrieve…
In our daily lives and industrial settings, we often encounter dynamic problems that require reasoning over time and metric constraints. These include tasks such as scheduling, routing, and production sequencing. Dynamic logics have…
Solving symbolic reasoning problems that require compositionality and systematicity is considered one of the key ingredients of human intelligence. However, symbolic reasoning is still a great challenge for deep learning models, which often…
We present a new type system with support for proofs of programs in a call-by-value language with control operators. The proof mechanism relies on observational equivalence of (untyped) programs. It appears in two type constructors, which…
We propose a framework for robust evaluation of reasoning capabilities of language models, using functional variants of benchmarks. Models that solve a reasoning test should exhibit no difference in performance over the static version of a…
Enhancing the mathematical reasoning of large language models (LLMs) demands high-quality training data, yet conventional methods face critical challenges in scalability, cost, and data reliability. To address these limitations, we propose…
While large language models (LLMs) have rapidly improved their performance on a broad number of tasks, they still often fall short on reasoning tasks. As LLMs become more integrated in diverse real-world tasks, advancing their reasoning…
The goal of this lecture is to show how modern theorem provers---in this case, the Coq proof assistant---can be used to mechanize the specification of programming languages and their semantics, and to reason over individual programs and…
Implementing a complex concept as an executable model in a strongly typed, purely functional language hits a sweet spot between mere simulation and formal specification. For research and education it is often desirable to enrich the…
We propose a purely extensional semantics for higher-order logic programming. In this semantics program predicates denote sets of ordered tuples, and two predicates are equal iff they are equal as sets. Moreover, every program has a unique…
The formal analysis of automated systems is an important and growing industry. This activity routinely requires new verification frameworks to be developed to tackle new programming features, or new considerations (bugs of interest). Often,…
Heuristic algorithms play a vital role in solving combinatorial optimization (CO) problems, yet traditional designs depend heavily on manual expertise and struggle to generalize across diverse instances. We introduce \textbf{HeurAgenix}, a…
Stepwise refinement of algebraic specifications is a well known formal methodology for program development. However, traditional notions of refinement based on signature morphisms are often too rigid to capture a number of relevant…
Functional logic languages are a high-level approach to programming by combining the most important declarative features. They abstract from small-step operational details so that programmers can concentrate on the logical aspects of an…