In praise of full meet contraction

Full meet contraction, that was devised by Carlos Alchourrón and David Makinson in the early 1980' s, has often been overlooked since it is not in itself a plausible contraction operator. However, it is a highly useful building-block in the construction of composite contraction operators. In particular, all plausible contraction operators can be reconstructed so that the outcome of contracting a belief set K by a sentence p is defined as K ∼ f (p), where ∼ is full meet contraction and f a sentential selector, i.e. a function to and from sentences. This paper investigates the logic of full meet contraction. Seven properties of this operation are presented that contribute to making it useful as a building-block: (1) Full meet contraction is a purely logical operation. (2) It retains finitebasedness of the belief set. (3) It is the inclusion-maximal contraction that removes all sentences that can contribute to implying the input sentence. (4) It is the inclusion-maximal contraction that removes all non-tautologous consequences of the input sentence. (5) Almost all contractions can be reconstructed as full meet contraction. (6) Full meet contraction allows for recovery of the input sentence. (7) Full meet contraction provides a unified account of multiple and singleton contractionLa llamada full meet contraction, creada por Carlos Alchourrón y David Makinson en los comienzos de los ' 80, ha sido a menudo desestimada puesto que ella no constituye un operador de contracción plausible. De todas formas ella es altamente útil en la construcción de operadores de contracción compuestos. En particular, todos los operadores de contracción plausibles pueden ser reconstruidos de forma tal que la contracción de un conjunto de creencias K por una sentencia p sea definida como K ∼ f(p), donde ∼ es una full meet contraction y f un selector de sentencias, i.e., una función de sentencias a sentencias. En este trabajo investigamos la lógica de la full meet contraction. Se presentan siete propiedades de esta operación que contribuyen a hacerla útil como building-block: (1) Full meet contraction es una operación puramente lógica.(2) Ella retiene la finit- basednes del conjunto de creencias.(3) Ella es la máxima-inclusiva de las contracciones que elimina todas las sentencias que pueden contribuir a implicar la input-sentence. (4) Es la contracción maximal inclusiva que elimina todas las consecuencias no tautológicas de la input-sentence. (5) Casi todas las contracciones pueden ser reconstruidas como full-meet contractions. (6) Full meet contraction permite la recuperación de la input-sentence.(7) Full meet contracción da cuenta en forma unificada de las contracciones múltiples y singulares

AGM 25 years: twenty-five years of research in belief change

The 1985 paper by Carlos Alchourrón (1931–1996), Peter Gärdenfors, and David Makinson (AGM), “On the Logic of Theory Change: Partial Meet Contraction and Revision Functions” was the starting-point of a large and rapidly growing literature that employs formal models in the investigation of changes in belief states and databases. In this review, the first twenty five years of this development are summarized. The topics covered include equivalent characterizations of AGM operations, extended representations of the belief states, change operators not included in the original framework, iterated change, applications of the model, its connections with other formal frameworks, computatibility of AGM operations, and criticism of the model.info:eu-repo/semantics/publishedVersio