Related papers: Computational interpretations of classical reasoni…
Computational Logic is the use of computers to establish facts in a logical formalism. Originating in 19th-century attempts to understand the nature of mathematical reasoning, the subject now comprises a wide variety of formalisms,…
In the rapidly growing literature on explanation algorithms, it often remains unclear what precisely these algorithms are for and how they should be used. In this position paper, we argue for a novel and pragmatic perspective: Explainable…
Several different proof translations exist between classical and intuitionistic logic (negative translations), and intuitionistic and linear logic (Girard translations). Our aims in this paper are (1) to consider extensions of…
This paper presents a soundness and completeness proof for propositional intuitionistic calculus with respect to the semantics of computability logic. The latter interprets formulas as interactive computational problems, formalized as games…
It has been shown that a functional interpretation of proofs in mathematical analysis can be given by the product of selection functions, a mode of recursion that has an intuitive reading in terms of the computation of optimal strategies in…
What is reasoning? This question has driven centuries of philosophical inquiry, from Aristotle's syllogisms to modern computational complexity theory. In the age of large language models achieving superhuman performance on benchmarks like…
Explanations of cognitive behavior often appeal to computations over representations. What does it take for a system to implement a given computation over suitable representational vehicles within that system? We argue that the language of…
Existing refinement calculi provide frameworks for the stepwise development of imperative programs from specifications. This paper presents a refinement calculus for deriving logic programs. The calculus contains a wide-spectrum logic…
This study examines the simulation of quantum algorithms on a classical computer. The program code implemented on a classical computer will be a straight connection between the mathematical formulation of quantum mechanics and computational…
Logic programming is a flexible programming paradigm due to the use of predicates without a fixed data flow. To extend logic languages with the compact notation of functional programming, there are various proposals to map evaluable…
Interpretational problems with quantum mechanics can be phrased precisely by only talking about empirically accessible information. This prompts a mathematical reformulation of quantum mechanics in terms of classical mechanics. We survey…
This article presents an overview of computability logic -- the game-semantically constructed logic of interactive computational tasks and resources. There is only one non-overview, technical section in it, devoted to a proof of the…
Logical reasoning is essential in a variety of human activities. A representative example of a logical task is mathematics. Recent large-scale models trained on large datasets have been successful in various fields, but their reasoning…
Computability logic is a formal theory of computability. The earlier article "Introduction to cirquent calculus and abstract resource semantics" by Japaridze proved soundness and completeness for the basic fragment CL5 of computability…
In this vision paper, we explore the challenges and opportunities of a form of computation that employs an empirical (rather than a formal) approach, where the solution of a computational problem is returned as empirically most likely…
Computability logic is a formal theory of computational tasks and resources. Formulas in it represent interactive computational problems, and "truth" is understood as algorithmic solvability. Interactive computational problems, in turn, are…
For building question answering systems and natural language interfaces, semantic parsing has emerged as an important and powerful paradigm. Semantic parsers map natural language into logical forms, the classic representation for many…
Scientists have demonstrated that quantum computing has presented novel approaches to address computational challenges, each varying in complexity. Adapting problem-solving strategies is crucial to harness the full potential of quantum…
We present a computer-supported approach for the logical analysis and conceptual explicitation of argumentative discourse. Computational hermeneutics harnesses recent progresses in automated reasoning for higher-order logics and aims at…
Many interesting and useful symbolic computation algorithms manipulate mathematical expressions in mathematically meaningful ways. Although these algorithms are commonplace in computer algebra systems, they can be surprisingly difficult to…