Related papers: Interpolation in Equilibrium Logic and Answer Set …
This chapter provides a comprehensive overview of proof-theoretic methods for establishing interpolation properties across a range of logics, including classical, intuitionistic, modal, and substructural logics. Central to the discussion…
The Boolean logic of subsets, usually presented as `propositional logic,' is considered as being "classical" while intuitionistic logic and the many sublogics and off-shoots are "non-classical." But there is another mathematical logic, the…
The sequential composition of propositional logic programs has been recently introduced. This paper studies the sequential {\em decomposition} of programs by studying Green's relations $\mathcal{L,R,J}$ -- well-known in semigroup theory --…
The decoupling between the representation of a certain problem, i.e., its knowledge model, and the reasoning side is one of main strong points of model-based Artificial Intelligence (AI). This allows, e.g. to focus on improving the…
When comparing inductive logic programming (ILP) and attribute-value learning techniques, there is a trade-off between expressive power and efficiency. Inductive logic programming techniques are typically more expressive but also less…
Nonlinear interpolants have been shown useful for the verification of programs and hybrid systems in contexts of theorem proving, model checking, abstract interpretation, etc. The underlying synthesis problem, however, is challenging and…
Translations between different nonmonotonic formalisms always have been an important topic in the field, in particular to understand the knowledge-representation capabilities those formalisms offer. We provide such an investigation in terms…
We address the problem of propositional logic-based abduction, i.e., the problem of searching for a best explanation for a given propositional observation according to a given propositional knowledge base. We give a general algorithm, based…
We show that Propositional Dynamic Logic (PDL) has the Craig Interpolation Property. This question has been open for many years. Three proof attempts were published, but later criticized in the literature or retracted. Our proof is based on…
Our position is that logic programming is not programming in the Horn clause sublogic of classical logic, but programming in a logic of (inductive) definitions. Thus, the similarity between prototypical Prolog programs (e.g., member,…
In the past decade the mathematical theory of machine learning has lagged far behind the triumphs of deep neural networks on practical challenges. However, the gap between theory and practice is gradually starting to close. In this paper I…
We study the fixed point property and the Craig interpolation property for sublogics of the interpretability logic $\mathbf{IL}$. We provide a complete description of these sublogics concerning the uniqueness of fixed points, the fixed…
Craig interpolation is a widespread method in verification, with important applications such as Predicate Abstraction, CounterExample Guided Abstraction Refinement and Lazy Abstraction With Interpolants. Most state-of-the-art model checking…
The unification of logic and probability is a long-standing concern in AI, and more generally, in the philosophy of science. In essence, logic provides an easy way to specify properties that must hold in every possible world, and…
Common model selection criteria, such as $AIC$ and its variants, are based on in-sample prediction error estimators. However, in many applications involving predicting at interpolation and extrapolation points, in-sample error cannot be…
The paper presents a method for obtaining problems whose conclusions contain disjunctive propositions. These problems constitute a version of inverse problems with a given logical structure. The logical models in the groups of problems…
LLMs show remarkable emergent abilities, such as inferring concepts from presumably out-of-distribution prompts, known as in-context learning. Though this success is often attributed to the Transformer architecture, our systematic…
Incrementality is ubiquitous in human-human interaction and beneficial for human-computer interaction. It has been a topic of research in different parts of the NLP community, mostly with focus on the specific topic at hand even though…
Unification of logic variables instantly connects present and future observations of their value, independently of their location in the data areas of the runtime system. The paper extends this property to "interclausal logic variables", an…
Probabilistic logic programs are logic programs in which some of the facts are annotated with probabilities. This paper investigates how classical inference and learning tasks known from the graphical model community can be tackled for…