Search results for "Conditional"
showing 10 items of 294 documents
Conditional connection explored: the case of Sicilian cusà
2022
Abstract Stemming from a wh-question, the Sicilian marker cusà (cu sa ‘who knows’) expresses several epistemic meanings, which can also reach the realm of conditionality. The paper explores the discourse profile of cusà as it emerges from the analysis of diachronic data (from the eighteenth and nineteenth centuries) and present-day informal Sicilian, namely spoken Sicilian and present-day informal Sicilian as written by speakers on the web. These data suggest a possible path of development leading from the wh-question to new functions. We propose that the origin of this development can be explained in the light of the strategy of the “impossible question”, while the diverse functions of cus…
Canonical Extensions of Conditional Probabilities and Compound Conditionals
2022
In this paper we show that the probability of conjunctions and disjunctions of conditionals in a recently introduced framework of Boolean algebras of conditionals are in full agreement with the corresponding operations of conditionals as defined in the approach developed by two of the authors to conditionals as three-valued objects, with betting-based semantics, and specified as suitable random quantities. We do this by first proving that the canonical extension of a full conditional probability on a finite algebra of events to the corresponding algebra of conditionals is compatible with taking subalgebras of events.
Iterated Conditionals, Trivalent Logics, and Conditional Random Quantities
2022
We consider some notions of iterated conditionals by checking the validity of some desirable basic logical and probabilistic properties, which are valid for simple conditionals. We consider de Finetti’s notion of conditional as a three-valued object and as a conditional random quantity in the betting framework. We recall the notions of conjunction and disjunction among conditionals in selected trivalent logics. Then, we analyze the two notions of iterated conditional introduced by Calabrese and de Finetti, respectively. We show that the compound probability theorem and other basic properties are not preserved by these objects, by also computing some probability propagation rules. Then, for …
Connexive Logic, Probabilistic Default Reasoning, and Compound Conditionals
2023
We present two approaches to investigate the validity of connexive principles and related formulas and properties within coherence-based probability logic. Connexive logic emerged from the intuition that conditionals of the form if not-A, then A, should not hold, since the conditional’s antecedent not-A contradicts its consequent A. Our approaches cover this intuition by observing that the only coherent probability assessment on the conditional event A | not-A is p(A | not-A) = 0. In the first approach we investigate connexive principles within coherence-based probabilistic default reasoning, by interpreting defaults and negated defaults in terms of suitable probabilistic constraints on con…
Algebraic aspects and coherence conditions for conjunctions among conditional events
2018
We deepen the study of a notion of conjunction among conditional events, introduced in previous papers in theframework of coherence. This notion of conjunction, differently from other approaches, is given in the setting ofconditional random quantities. We show that some well known properties which are satisfied by conjunctionsof unconditional events are also satisfied by conjunctions of conditional events. In particular we examine anadditive property and a decomposition formula, by also obtaining a generalized inclusion-exclusion formula. Then,by exploiting the notion of conjunction, we introduce the set of constituents generated bynconditional events.Moreover, under logical independence, w…
Logical Operations among Conditional Events: theoretical aspects and applications
2019
We generalize the notions of conjunction and disjunction of two conditional events to the case of $n$ conditional events. These notions are defined, in the setting of coherence, by means of suitable conditional random quantities with values in the interval $[0,1]$. We also define the notion of negation, by verifying De Morgan's Laws. Then, we give some results on coherence of prevision assessments for some families of compounded conditionals and we show that some well known properties which are satisfied by conjunctions and disjunctions of unconditional events are also satisfied by conjunctions and disjunction of conditional events. We also examine in detail the coherence of the prevision a…
Generalized coherence and connection property of imprecise conditional previsions.
2008
In this paper we consider imprecise conditional prevision assessments on random quantities with finite set of possible values. We use a notion of generalized coherence which is based on the coherence principle of de Finetti. We consider the checking of g-coherence, by extending some previous results obtained for imprecise conditional probability assessments. Then, we study a connection property of interval-valued gcoherent prevision assessments, by extending a result given in a previous paper for precise assessments.
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 Fr'echet-Hoeffding bounds. Moreover, we study the reverse probabilistic inference from the conjunction $mathc…
Compounds of conditionals and iterated conditioning under coherence
2017
We discuss the problem of defining logical operations among conditional events. Differently from many authors, we define the conjunction and disjunction in the setting of conditional random quantities. In probability theory and in probability logic a relevant problem, largely discussed by many authors, is that of defining logical operations among conditional events. In the many works concerning these operations, the conjunction and disjunction have been usually defined as suitable conditional events. In Kaufmann 2009 it has been proposed a theory for the compounds of conditionals which has been framed in the setting of coherence in (Gilio and Sanfilippo , 2013, 2014) In this framework, whic…
On compound and iterated conditionals
2021
We illustrate the notions of compound and iterated conditionals introduced, in recent papers, as suitable conditional random quantities, in the framework of coherence. We motivate our definitions by examining some concrete examples. Our logical operations among conditional events satisfy the basic probabilistic properties valid for unconditional events. We show that some, intuitively acceptable, compound sentences on conditionals can be analyzed in a rigorous way in terms of suitable iterated conditionals. We discuss the Import-Export principle, which is not valid in our approach, by also examining the inference from a material conditional to the associated conditional event. Then, we illus…