Related papers: A survey of paraconsistent logics
We analyse a specific instance of the general approach of reasoning based on forgetting by Lang and Marquis. More precisely, we discuss an approach for reasoning with inconsistent information using maximal consistent subsignatures, where a…
We extend the simply-typed guarded $\lambda$-calculus with discrete probabilities and endow it with a program logic for reasoning about relational properties of guarded probabilistic computations. This provides a framework for programming…
There are several contexts of non-monotonic reasoning where a priority between rules is established whose purpose is preventing conflicts. One formalism that has been widely employed for non-monotonic reasoning is the sceptical one known as…
The KLM approach to defeasible reasoning introduces a weakened form of implication into classical logic. This allows one to incorporate exceptions to general rules into a logical system, and for old conclusions to be withdrawn upon learning…
Nonmonotonic logics are usually characterized by the presence of some notion of 'conditional' that fails monotonicity. Research on nonmonotonic logics is therefore largely concerned with the defeasibility of argument forms and the…
This paper is an extended version of an earlier submission to WoLLIC 2023. We discuss two-layered logics formalising reasoning with probabilities and belief functions that combine the Lukasiewicz $[0,1]$-valued logic with Baaz $\triangle$…
We start in this work the study of the relation between the theory of regularity structures and paracontrolled calculus. We give a paracontrolled representation of the reconstruction operator and provide a natural parametrization of the…
Adjoint logic is a general approach to combining multiple logics with different structural properties, including linear, affine, strict, and (ordinary) intuitionistic logics, where each proposition has an intrinsic mode of truth. It has…
Calibration, which establishes the correlation between accuracy and model confidence, is important for LLM development. We design three off-the-shelf calibration methods based on self-consistency (Wang et al., 2022) for math reasoning…
First we introduce the Bailleul-Hoshino's result [4], which links the theory of regularity structures and the paracontrolled calculus. As an application of their result, we give another algebraic proof of the multicomponent commutator…
Possibilistic logic is a well-known graded logic of uncertainty suitable to reason under incomplete information and partially inconsistent knowledge, which is built upon classical first order logic. There exists for Possibilistic logic a…
Large language models (LLMs) have achieved widespread success on a variety of in-context few-shot tasks, but this success is typically evaluated via correctness rather than consistency. We argue that self-consistency is an important…
The `catuskoti' or tetralemma in Buddhist logic is a problematic subject from the modern logical point of view. Recently a many-valued paraconsistent logic was proposed in order to formalize catuskoti adequately by G. Priest. On the other…
As of the date of this version, this monograph (parts I and II) contains all of the known technical results relative to the Robinson-styled nonstandard modeling of natural languages and certain associated linguistic processes such as…
This paper constructs a cirquent calculus system and proves its soundness and completeness with respect to the semantics of computability logic (see http://www.cis.upenn.edu/~giorgi/cl.html). The logical vocabulary of the system consists of…
Propositional Typicality Logic (PTL) is a recently proposed logic, obtained by enriching classical propositional logic with a typicality operator capturing the most typical (alias normal or conventional) situations in which a given sentence…
In 1952 P. F. Strawson proposed a logic of presuppositions. It is an interpretation of Aristotelian logic, i.e. of the logic of the traditional syllogism. In 1981 Richard Diaz published a monograph in which he presented truth-relevant…
In this survey, we present in a unified way the categorical and syntactical settings of coherent differentiation introduced recently, which shows that the basic ideas of differential linear logic and of the differential lambda-calculus are…
The purpose of this paper is to develop further the main concepts of Phenomena Dynamic Logic (P-DL) and Cognitive Dynamic Logic (C-DL), presented in the previous paper. The specific character of these logics is in matching vagueness or…
We introduce a variant of Dependence Logic in which truth is defined not in terms of existence of winning strategies for the Proponent (Eloise) in a semantic game, but in terms of lack of winning strategies for the Opponent (Abelard). We…