Related papers: Constructive Game Logic
Constructor-Based Conditional Rewriting Logic is a general framework for integrating first-order functional and logic programming which gives an algebraic semantics for non-deterministic functional-logic programs. In the context of this…
The present work aims to give a unity of logic via standard sequential, unpolarized games. Specifically, our vision is that there must be mathematically precise concepts of linear refinement and intuitionistic restriction of logic such that…
While Large Language Models have achieved notable success on formal mathematics benchmarks such as MiniF2F, it remains unclear whether these results stem from genuine logical reasoning or semantic pattern matching against pre-training data.…
Whether it be in normal form games, or in fair allocations, or in voter preferences in voting systems, a certain pattern of reasoning is common. From a particular profile, an agent or a group of agents may have an incentive to shift to a…
In this paper, we introduce game-theoretic semantics (GTS) for Qualitative Choice Logic (QCL), which, in order to express preferences, extends classical propositional logic with an additional connective called ordered disjunction. Firstly,…
In the context of strategic games, we provide an axiomatic proof of the statement Common knowledge of rationality implies that the players will choose only strategies that survive the iterated elimination of strictly dominated strategies.…
We describe the design and implementation of a reasoning engine that facilitates the gamification of loop-invariant discovery. Our reasoning engine enables students, computational agents and regular software engineers with no formal methods…
Game semantics is a powerful method of semantic analysis for programming languages. It gives mathematically accurate models ("fully abstract") for a wide variety of programming languages. Game semantic models are combinatorial…
In this dissertation we provide mathematical evidence that the concept of learning can be used to give a new and intuitive computational semantics of classical proofs in various fragments of Predicative Arithmetic. First, we extend Kreisel…
This dissertation explores the roles of polarities and focussing in various aspects of Computational Logic. These concepts play a key role in the the interpretation of proofs as programs, a.k.a. the Curry-Howard correspondence, in the…
The interactive game theoretical approach to tactics and behavioral self-organization is developed. Though it uses the interactive game theoretical formalization of dialogues as psycholinguistic phenomena, the crucial role is played by the…
This is the author's Ph.D. Thesis. It contains results from four years of research into realizability and categorical logic. The main subjects are the axiomatisation of realizable propositions, and a characterization of realizability…
We consider a simple extension of logic programming where variables may range over goals and goals may be arguments of predicates. In this language we can write logic programs which use goals as data. We give practical evidence that, by…
The paper describes an extension of well-founded semantics for logic programs with two types of negation. In this extension information about preferences between rules can be expressed in the logical language and derived dynamically. This…
Recently, we had to realize that more and more game theoretical articles have been published in peer-reviewed journals with severe logical deficiencies. In particular, we observed that the indirect proof was not applied correctly. These…
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…
The generation of comprehensible explanations is an essential feature of modern artificial intelligence systems. In this work, we consider probabilistic logic programming, an extension of logic programming which can be useful to model…
Large Language Models (LLMs) have revolutionized natural language processing, yet they struggle with inconsistent reasoning, particularly in novel domains and complex logical sequences. This research introduces Proof of Thought, a framework…
Logic can be made useful for programming and for databases independently of logic programming. To be useful in this way, logic has to provide a mechanism for the definition of new functions and new relations on the basis of those given in…
The work is devoted to Computability Logic (CoL) -- the philosophical/mathematical platform and long-term project for redeveloping classical logic after replacing truth} by computability in its underlying semantics (see…