Related papers: A Calculus of Inconsistency I: Sentential Logic
We make explicit the correspondence between syntax and syntactic categories for coherent first-order logic, providing a categorical characterization of bi-interpretability. This is done by creating a biequivalence between a bicategory of…
An alternative proof of the completeness of relational algebra with respect to allowed formulas of first-order logic is presented. The proof relies on the well-known embedding of relational algebra into cylindric algebra, which makes it…
We consider a modal logic that can formalise statements about uncertainty and beliefs such as `I think that my wallet is in the drawer rather than elsewhere' or `I am confused whether my appointment is on Monday or Tuesday'. To do that, we…
We consider a simple modal logic whose non-modal part has conjunction and disjunction as connectives and whose modalities come in adjoint pairs, but are not in general closure operators. Despite absence of negation and implication, and of…
Explanations are an important tool for gaining insights into the behavior of ML models, calibrating user trust and ensuring regulatory compliance. Past few years have seen a flurry of post-hoc methods for generating model explanations, many…
In this paper we address the problem of handling inconsistencies in tables with missing values (also called nulls) and functional dependencies. Although the traditional view is that table instances must respect all functional dependencies…
In this note we discuss a variant of linear logic with idempotent exponential modalities. We propose a sequent calculus system and discuss its semantics. We also give a concrete relational model for this calculus.
Large Language Models (LLMs) have impressive capabilities, but are prone to outputting falsehoods. Recent work has developed techniques for inferring whether a LLM is telling the truth by training probes on the LLM's internal activations.…
It is well-known that Choice and Regularity are independent of each other but have important common consequences of logical character (reflection principles, representations of classes by sets, etc.). We explain this phenomenon by isolating…
We give a proof-theoretic as well as a semantic characterization of a logic in the signature with conjunction, disjunction, negation, and the universal and existential quantifiers that we suggest has a certain fundamental status. We present…
The main subjects of this text are: (1) Generalization of concepts and operations, like distance and size, to situations where they are not definable in the usual way. (2) A pragmatic theory of handling contradictions using reliability of…
A major reason behind the success of probability calculus is that it possesses a number of valuable tools, which are based on the notion of probabilistic independence. In this paper, I identify a notion of logical independence that makes…
Drawing appropriate defeasible inferences has been proven to be one of the most pervasive puzzles of natural language processing and a recurrent problem in pragmatics. This paper provides a theoretical framework, called ``stratified…
The compactness theorem for a logic states, roughly, that the satisfiability of a set of well-formed formulas can be determined from the satisfiability of its finite subsets, and vice versa. Usually, proofs of this theorem depend on the…
We obtain, for the first time, a modular many-valued semantics for combined logics, which is built directly from many-valued semantics for the logics being combined, by means of suitable universal operations over partial non-deterministic…
Sequential propositional logic deviates from ordinary propositional logic by taking into account that during the sequential evaluation of a propositional statement,atomic propositions may yield different Boolean values at repeated…
The definition of stable models for propositional formulas with infinite conjunctions and disjunctions can be used to describe the semantics of answer set programming languages. In this note, we enhance that definition by introducing a…
Reasoning semantically in first-order logic is notoriously a challenge. This paper surveys a selection of semantically-guided or model-based methods that aim at meeting aspects of this challenge. For first-order logic we touch upon…
In this work, we develop a formal system of inductive logic. It uses an infinitary language that allows for countable conjunctions and disjunctions. It is based on a set of nine syntactic rules of inductive inference, and contains classical…
Defeasible logic is an efficient logic for defeasible reasoning. It is defined through a proof theory and, until now, has had no model theory. In this paper a model-theoretic semantics is given for defeasible logic. The logic is sound and…