相关论文: Admissibility in Positive Logics

We give a procedure for counting the number of different proofs of a formula in various sorts of propositional logic. This number is either an integer (that may be 0 if the formula is not provable) or infinite.

The language of probability is used to define several different types of conditional statements. There are four principal types: subjunctive, material, existential, and feasibility. Two further types of conditionals are defined using the…

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…

Several open problems in algebraic logic are solved.

Egalitarian considerations play a central role in many areas of social choice theory. Applications of egalitarian principles range from ensuring everyone gets an equal share of a cake when deciding how to divide it, to guaranteeing balance…

Extended multi-adjoint logic programming arises as an extension of multi-adjoint normal logic programming where constraints and a special type of aggregator operator have been included. The use of this general aggregator operator permits to…

Prediction problems often admit competing models that perform almost equally well. This effect challenges key assumptions in machine learning when competing models assign conflicting predictions. In this paper, we define predictive…

Admissable weight is an important tool for studying spectral invariance in operator algebra. Common admissable weights include polynomial weights and sub exponential weights. This article mainly provides a proof that polynomial weights are…

We extend dynamic logic of propositional assignments by adding an operator of parallel composition that is inspired by separation logics. We provide an axiomatisation via reduction axioms, thereby establishing decidability. We also prove…

An exhaustive survey of categorical propositions is proposed in the present paper, both with respect to their nature and the logical problems raised by them. Through a comparative analysis of Term Logic and First-Order Logic, it is shown…

We study comparisons between interpretations in description logics with respect to "logical consequences" of the form of semi-positive concepts (like semi-positive concept assertions). Such comparisons are characterized by conditions…

In the paper, the idea of describing not-yet-verified properties of quantum objects with logical many-valuedness is scrutinized. As it is argued, to promote such an idea, the following two foundational problems of many-valued quantum logic…

We give an overview of some developments in dependence and independence logic. This is a tiny selection, intended for a newcomer, from a rapidly growing literature on the topic. Furthermore, we discuss conditional independence atoms and we…

Checking the admissibility of quasiequations in a finitely generated (i.e., generated by a finite set of finite algebras) quasivariety Q amounts to checking validity in a suitable finite free algebra of the quasivariety, and is therefore…

Let K be a number field. A finite group G is called K-admissible if there exists a G-crossed product K-division algebra. K-admissibility has a necessary condition called K-preadmissibility that is known to be sufficient in many cases. It is…

Probabilistic independence is a useful concept for describing the result of random sampling---a basic operation in all probabilistic languages---and for reasoning about groups of random variables. Nevertheless, existing verification methods…

We develop a general criterion for cut elimination in sequent calculi for propositional modal logics, which rests on absorption of cut, contraction, weakening and inversion by the purely modal part of the rule system. Our criterion applies…

Humans currently use arguments for explaining choices which are already made, or for evaluating potential choices. Each potential choice has usually pros and cons of various strengths. In spite of the usefulness of arguments in a decision…

We present a proof system that extends action logic by omega iteration, which is viewed as infinitary multiplicative conjunction. We prove cut admissibility and establish complexity bounds for the provability predicate.

Linear logic was conceived in 1987 by Girard and, in contrast to classical logic, restricts the usage of the structural inference rules of weakening and contraction. With this, atoms of the logic are no longer interpreted as truth, but as…