Related papers: Ludics and its Applications to natural Language Se…
Cathoristic logic is a multi-modal logic where negation is replaced by a novel operator allowing the expression of incompatible sentences. We present the syntax and semantics of the logic including complete proof rules, and establish a…
Most natural language processing tasks require lexical semantic information. Automated acquisition of this information would thus increase the robustness and portability of NLP systems. This paper describes an acquisition method which makes…
This is a short paper about the relationship between logic and computation. More specifically, it is about a relationship between the completeness proof for intuitionistic propositional logic within the form of proof-theoretic semantics…
Classical higher-order logic, when utilized as a meta-logic in which various other (classical and non-classical) logics can be shallowly embedded, is well suited for realising a universal logic reasoning approach. Universal logic reasoning…
We investigate the expressive power of a Turing-complete logic based on game-theoretic semantics. By defining suitable fragments and variants of the logic, we obtain a range of natural characterizations for some fundamental families of…
The purpose of this paper is to introduce justification logics based on conditional logics. We introduce a new family of logics, called conditional justification logics, which incorporates a counterfactual conditional in its language. For…
Game semantics is a trace-like denotational semantics for programming languages where the notion of legal observable behaviour of a term is defined combinatorially, by means of rules of a game between the term (the "Proponent") and its…
We present an algebraic view on logic programming, related to proof theory and more specifically linear logic and geometry of interaction. Within this construction, a characterization of logspace (deterministic and non-deterministic)…
Classes of linguistic paradoxes and linguistic tautologies are introduced with examples and explanations. They are part of the author's work on the Paradoxist Philosophy based on mathematical logic. The general cases exposed below are…
The field of proof-theoretic semantics (P-tS) offers an alternative approach to meaning in logic that is based on inference and argument (rather than truth in a model). It has been successfully developed for various logics; in particular,…
How does one measure "ability to understand language"? If it is a person's ability that is being measured, this is a question that almost never poses itself in an unqualified manner: Whatever formal test is applied, it takes place on the…
After the social learning models were proposed, finding the solutions of the games becomes a well-defined mathematical question. However, almost all papers on the games and their applications are based on solutions built upon either an…
We introduce operational semantics into games. And based on the operational semantics, we establish a full algebra of games, including basic algebra of games, algebra of concurrent games, recursion and abstraction. The algebra can be used…
We extend the meet-implication fragment of propositional intuitionistic logic with a meet-preserving modality. We give semantics based on semilattices and a duality result with a suitable notion of descriptive frame. As a consequence we…
In Dung-style abstract argumentation, various semantics capture notions of acceptability of arguments. The admissibility semantics capture the notion that an argument can be consistently defended from any potential counterargument. Weak…
Mathematical text is written using a combination of words and mathematical expressions. This combination, along with a specific way of structuring sentences makes it challenging for state-of-art NLP tools to understand and reason on top of…
We introduce a logic for reasoning about evidence, that essentially views evidence as a function from prior beliefs (before making an observation) to posterior beliefs (after making the observation). We provide a sound and complete…
Our understanding about things is conceptual. By stating that we reason about objects, it is in fact not the objects but concepts referring to them that we manipulate. Now, so long just as we acknowledge infinitely extending notions such as…
At the heart of intuitionistic type theory lies an intuitive semantics called the "meaning explanations"; crucially, when meaning explanations are taken as definitive for type theory, the core notion is no longer "proof" but "verification".…
I explore some of the issues that arise when trying to establish a connection between the underspecification hypothesis pursued in the NLP literature and work on ambiguity in semantics and in the psychological literature. A theory of…