Related papers: Why Bother With Syntax?
The present article is a brief informal survey of computability logic --- the game-semantically conceived formal theory of computational resources and tasks. This relatively young nonclassical logic is a conservative extension of classical…
Belief revision has been studied mainly with respect to background logics that are monotonic in character. In this paper we study belief revision when the underlying logic is non-monotonic instead--an inherently interesting problem that is…
The tension between deduction and induction is perhaps the most fundamental issue in areas such as philosophy, cognition and artificial intelligence (AI). The deduction camp concerns itself with questions about the expressiveness of formal…
Dialectical logic is the logic of dialectical processes. The goal of dialectical logic is to introduce dynamic notions into logical computational systems. The fundamental notions of proposition and truth-value in standard logic are subsumed…
Proofs, in Ludics, have an interpretation provided by their counter-proofs, that is the objects they interact with. We follow the same idea by proposing that sentence meanings are given by the counter-meanings they are opposed to in a…
While syntactic inference restrictions don't play an important role for SAT, they are an essential reasoning technique for more expressive logics, such as first-order logic, or fragments thereof. In particular, they can result in short…
Logic programming with fixed-point definitions is a useful extension of traditional logic programming. Fixed-point definitions can capture simple model checking problems and closed-world assumptions. Its operational semantics is typically…
Logic rules and inference are fundamental in computer science and have been studied extensively. However, prior semantics of logic languages can have subtle implications and can disagree significantly, on even very simple programs,…
A hundred years ago, logic was almost synonymous with foundational studies. The ongoing AI revolution raises many deep foundational problems involving neuroscience, philosophy, computer science, and logic. The goal of the following dialog…
Reasoning is an essential skill to enable Large Language Models (LLMs) to interact with the world. As tasks become more complex, they demand increasingly sophisticated and diverse reasoning capabilities for sequential decision-making,…
Computer programs are often factored into pure components -- simple, total functions from inputs to outputs -- and components that may have side effects -- errors, changes to memory, parallel threads, abortion of the current loop, etc. We…
Formalizing syntactic proofs of properties of logics, programming languages, security protocols, and other formal systems is a significant challenge, in large part because of the obligation to handle name-binding correctly. We present an…
As a contribution to the challenge of building game-playing AI systems, we develop and analyse a formal language for representing and reasoning about strategies. Our logical language builds on the existing general Game Description Language…
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…
This article is devoted to the tactical game theoretical interpretation of dialectics. Dialectical games are considered as abstractly as well as models of the internal dialogue and reflection. The models related to the representation theory…
Semantic communication (SC) goes beyond technical communication in which a given sequence of bits or symbols, often referred to as information, is be transmitted reliably over a noisy channel, regardless of its meaning. In SC, conveying the…
Answer substitutions play a central role in logic programming. To support {\it selective} answer substitutions, we refine $\exists x$ in goals into two different versions: the noisy version $\exists^o x$ and the silent version $\exists x$.…
When a decision, such as the approval or denial of a bank loan, is delegated to a computer, an explanation of that decision ought to be given with it. This ethical need to explain the decisions leads to the search for a formal definition of…
Rules in logic programming encode information about mutual interdependencies between literals that is not captured by any of the commonly used semantics. This information becomes essential as soon as a program needs to be modified or…
Contemporary semantic description of logic is based on the ontology of all possible interpretations, an insufficiently clear metaphysical concept. In this article, logic is described as the internal organization of language. Logical…