Search results for "Rule of inference"
showing 10 items of 10 documents
What do we mean by diversity? : the path towards quantification
2018
The concept of biological diversity has evolved from a simple count of species to more sophisticated measures that are sensitive to relative abundances and even to evolutionary divergence times between species. In the course of this evolution, diversity measures have often been borrowed from other disciplines. Biological reasoning about diversity often implicitly assumed that measures of diversity had certain mathematical properties, but most of biologys traditional diversity measures did not actually possess these properties, a situation which often led to mathematically and biologically invalid inferences. Biologists now usually transform the traditional measures to the «effective number …
Awareness and Partitional Informational Structures
1997
We begin with an example to motivate the introduction of the concept of unawareness in models of information. There are a subject and two possible states of the world, σ and τ. At σ a certain fact p happens — it is true — and the subject sees it or hears it or anyhow perceives it, so that he knows it is true (in Geanakoplos [5] the subject is Sherlock Holmes’ assistant and fact p is ‘the dog barks’). At state τ fact p does not occur (it is false), and the subject not only does not see it or hear it etc.; but what is more, he does not even think of the possibility that it might: fact p is not present to the subject’s mind. What is an appropriate formal model for this story?
Collection Principles in Dependent Type Theory
2002
We introduce logic-enriched intuitionistic type theories, that extend intuitionistic dependent type theories with primitive judgements to express logic. By adding type theoretic rules that correspond to the collection axiom schemes of the constructive set theory CZF we obtain a generalisation of the type theoretic interpretation of CZF. Suitable logic-enriched type theories allow also the study of reinterpretations of logic. We end the paper with an application to the double-negation interpretation.
Generalized probabilistic modus ponens
2017
Modus ponens (from A and “if A then C” infer C) is one of the most basic inference rules. The probabilistic modus ponens allows for managing uncertainty by transmitting assigned uncertainties from the premises to the conclusion (i.e., from P(A) and P(C|A) infer P(C)). In this paper, we generalize the probabilistic modus ponens by replacing A by the conditional event A|H. The resulting inference rule involves iterated conditionals (formalized by conditional random quantities) and propagates previsions from the premises to the conclusion. Interestingly, the propagation rules for the lower and the upper bounds on the conclusion of the generalized probabilistic modus ponens coincide with the re…
Unawareness and Partitional Information Structures
1999
Abstract We claim first that simple uncertainty is not an adequate model of a subject's ignorance, because a major component of it is the inability to give a complete description of the states of the world, and we provide a formal model of unawareness. In Modica and Rustichini (1994) we showed a difficulty in the project, namely that without weakening of the inference rules of the logic one would face the unpleasant alternative between full awareness and full unawareness. In this paper we study a logical system where non full awareness is possible, and prove that a satisfactory solution to the problem can be found by introducing limited reasoning ability of the subject. A determination theo…
Local Monitor Implementation for Decentralized Intrusion Detection in Secure Multi–Agent Systems
2007
This paper focuses on the detection of misbehav- ing agents within a group of mobile robots. A novel approach to automatically synthesize a decentralized Intrusion Detection System (IDS) as well as an efficient implementation of local monitors are presented. In our scenario, agents perform possi- bly different independent tasks, but cooperate to guarantee the entire system’s safety. Indeed, agents plan their next actions by following a set of logic rules which is shared among them. Such rules are decentralized, i.e. they depend only on configurations of neighboring agents. However, some agents may not be acting according to this cooperation protocol, due to spontaneous failure or tampering.…
Generalized Logical Operations among Conditional Events
2018
We generalize, by a progressive procedure, the notions of conjunction and disjunction of two conditional events to the case of n conditional events. In our coherence-based approach, conjunctions and disjunctions are suitable conditional random quantities. We define the notion of negation, by verifying De Morgan’s Laws. We also show that conjunction and disjunction satisfy the associative and commutative properties, and a monotonicity property. Then, we give some results on coherence of prevision assessments for some families of compounded conditionals; in particular we examine the Frechet-Hoeffding bounds. Moreover, we study the reverse probabilistic inference from the conjunction $\mathcal…
Quasi conjunction, quasi disjunction, t-norms and t-conorms: Probabilistic aspects
2013
We make a probabilistic analysis related to some inference rules which play an important role in nonmonotonic reasoning. In a coherence-based setting, we study the extensions of a probability assessment defined on $n$ conditional events to their quasi conjunction, and by exploiting duality, to their quasi disjunction. The lower and upper bounds coincide with some well known t-norms and t-conorms: minimum, product, Lukasiewicz, and Hamacher t-norms and their dual t-conorms. On this basis we obtain Quasi And and Quasi Or rules. These are rules for which any finite family of conditional events p-entails the associated quasi conjunction and quasi disjunction. We examine some cases of logical de…
Logical Sentential Calculi Inspired by the Chrysippean Sentential Calculus
2021
The aim of the present paper is to consider an approach, different from that presented by J. Łukasiewicz, concerning the interpretation of the so-called stoic undemonstrables, which were given by Chrysippus. Stoic undemonstrables have been interpreted in two different ways: using the notion of “negation of a sentence” (Łukasiewicz) and using the notion of “a sentence inconsistent with a given one” (Mates). According to the Stoics, two sentences are inconsistent if one of them is negation of the other. The Mates’ interpretation generates five different inference rules. Based on one of these rules we can consider (with other undemonstrables) four different stoic propositional calculi. Taking …
A systematic approach to deriving incremental type checkers
2020
Static typing can guide programmers if feedback is immediate. Therefore, all major IDEs incrementalize type checking in some way. However, prior approaches to incremental type checking are often specialized and hard to transfer to new type systems. In this paper, we propose a systematic approach for deriving incremental type checkers from textbook-style type system specifications. Our approach is based on compiling inference rules to Datalog, a carefully limited logic programming language for which incremental solvers exist. The key contribution of this paper is to discover an encoding of the infinite typing relation as a finite Datalog relation in a way that yields efficient incremental up…