Related papers: How to Make a New Logic

We present a completeness result for a logical system which combines stit logic and justification logic in order to represent proving activity of the agents. This logic is interpreted over the semantics introduced in earlier publications.…

In traditional justification logic, evidence terms have the syntactic form of polynomials, but they are not equipped with the corresponding algebraic structure. We present a novel semantic approach to justification logic that models…

Recent work (Ross et al., 2025, 2024) has argued that the ability of humans and LLMs respectively to generalize to novel adjective-noun combinations shows that they each have access to a compositional mechanism to determine the phrase's…

Theorem proving is one of the oldest applications which require heuristics to prune the search space. Invertible proof procedures has been the major tool. In this paper, we present a novel and powerful heuristic called $nongshim$ which can…

Justification logics are an explication of modal logic; boxes are replaced with proof terms formally through realisation theorems. This can be achieved syntactically using a cut-free proof system e.g. using sequent, hypersequent or nested…

We prove that given two cut free nets of linear logic, by means of their relational interpretations one can: 1) first determine whether or not the net obtained by cutting the two nets is strongly normalizable 2) then (in case it is strongly…

Deontic logics are formalisms for reasoning over norms, obligations, permissions and prohibitions. Input/Output (I/O) Logics are a particular family of so-called norm-based deontic logics that formalize conditional norms outside of the…

The rationalizability concept was introduced in \cite{Ber84} and \cite{Pea84} to assess what can be inferred by rational players in a non-cooperative game in the presence of common knowledge. However, this notion can be defined in a number…

The notion of argumentation and the one of belief stand in a problematic relation to one another. On the one hand, argumentation is crucial for belief formation: as the outcome of a process of arguing, an agent might come to (justifiably)…

In rule-based systems, goal-oriented computations correspond naturally to the possible ways that an observation may be explained. In some applications, we need to compute explanations for a series of observations with the same domain. The…

Justification logics are modal-like logics with the additional capability of recording the reason, or justification, for modalities in syntactic structures, called justification terms. Justification logics can be seen as explicit…

The semantic foundations for logic programming are usually separated into two different approaches. The operational semantics, which uses SLD-resolution, the proof method that computes answers in logic programming, and the declarative…

Many large language models (LLMs) use reasoning to generate responses but do not reveal their full reasoning traces (a.k.a. chains of thought), instead outputting only final answers and brief reasoning summaries. To demonstrate that hiding…

In \cite{LC, LCMF}, it was introduced a logic (called \Six ) associated to a class of algebraic structures known as {\em involutive Stone algebras}. This class of algebras, denoted by \Sto , was considered by the first time in \cite{CS1} as…

In the philosophical tradition of `analytic pragmatism', which attempts to account for linguistic meanings in terms of their practices of use, logical expressivism is a theory which offers a distinct perspective on logic. We shed light on…

The features of a logically sound approach to a theory of statistical reasoning are discussed. A particular approach that satisfies these criteria is reviewed. This is seen to involve selection of a model, model checking, elicitation of a…

Since Austin introduced the term ``infelicity'', the linguistic literature has been flooded with its use, but no formal or computational explanation has been given for it. This thesis provides one for those infelicities that occur when a…

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…

This paper develops an algorithmic-based approach for proving inductive properties of propositional sequent systems such as admissibility, invertibility, cut-elimination, and identity expansion. Although undecidable in general, these…

Writers generally rely on plans or sketches to write long stories, but most current language models generate word by word from left to right. We explore coarse-to-fine models for creating narrative texts of several hundred words, and…