Related papers: Support is Search
Higher-order constructs extend the expressiveness of first-order (Constraint) Logic Programming ((C)LP) both syntactically and semantically. At the same time assertions have been in use for some time in (C)LP systems helping programmers…
Logical relations are one of the most powerful techniques in the theory of programming languages, and have been used extensively for proving properties of a variety of higher-order calculi. However, there are properties that cannot be…
In this contribution we revisit regular model checking, a powerful framework that has been successfully applied for the verification of infinite-state systems, especially parameterized systems (concurrent systems with an arbitrary number of…
We extend Lawvere-Pitts prop-categories (aka. hyperdoctrines) to develop a general framework for providing "algebraic" semantics for nonclassical first-order logics. This framework includes a natural notion of substitution, which allows…
Uniform proofs are sequent calculus proofs with the following characteristic: the last step in the derivation of a complex formula at any stage in the proof is always the introduction of the top-level logical symbol of that formula. We…
Answer-set programming (ASP) paradigm is a way of using logic to solve search problems. Given a search problem, to solve it one designs a theory in the logic so that models of this theory represent problem solutions. To compute a solution…
The overall goal of this paper is to investigate the theoretical foundations of algorithmic verification techniques for first order linear logic specifications. The fragment of linear logic we consider in this paper is based on the linear…
We study the completeness problem for propositionally quantified modal logics on quantifiable general frames, where the admissible sets are the propositions the quantifiers can range over and expressible sets of worlds are admissible, and…
This paper proposes an alternative to standard first-order logic that seeks greater naturalness, generality, and semantic self-containment. The system removes the first-order restriction, avoids type hierarchies, and dispenses with external…
Prawitz conjectured that the proof-theoretically valid logic is intuitionistic logic. Recent work on proof-theoretic validity has disproven this. In fact, it has been shown that proof-theoretic validity is not even closed under…
The study of Description Logics have been historically mostly focused on features that can be translated to decidable fragments of first-order logic. In this paper, we leave this restriction behind and look for useful and decidable…
The definition is a common form of human expert knowledge, a building block of formal science and mathematics, a foundation for database theory and is supported in various forms in many knowledge representation and formal specification…
We present a probabilistic version of PCF, a well-known simply typed universal functional language. The type hierarchy is based on a single ground type of natural numbers. Even if the language is globally call-by-name, we allow a…
A fundamental question asked in modal logic is whether a given theory is consistent. But consistent with what? A typical way to address this question identifies a choice of background knowledge axioms (say, S4, D, etc.) and then shows the…
The automated proof search system and decidability for logic of correlated knowledge is presented in this paper. The core of the proof system is the sequent calculus with the properties of soundness, completeness, admissibility of cut and…
We introduce the logic FOCN(P) which extends first-order logic by counting and by numerical predicates from a set P, and which can be viewed as a natural generalisation of various counting logics that have been studied in the literature. We…
Generative AI tools often answer questions using source documents, e.g., through retrieval augmented generation. Current groundedness and hallucination evaluations largely frame the relationship between an answer and its sources as binary…
Recent authors have proposed analyzing conditional reasoning through a notion of intervention on a simulation program, and have found a sound and complete axiomatization of the logic of conditionals in this setting. Here we extend this…
The present work presents some results about the categorial relation between logics and its categories of structures. A (propositional, finitary) logic is a pair given by a signature and Tarskian consequence relation on its formula algebra.…
Linearizability is a standard correctness criterion for concurrent algorithms, typically proved by establishing the algorithms' linearization points. However, relying on linearization points leads to proofs that are…