143 research outputs found
The Epistemology of Modality
This article surveys recent developments in the epistemology of modality
Probabilistic entailment and iterated conditionals
In this paper we exploit the notions of conjoined and iterated conditionals,
which are defined in the setting of coherence by means of suitable conditional
random quantities with values in the interval . We examine the iterated
conditional , by showing that p-entails if and only if
. Then, we show that a p-consistent family
p-entails a conditional event if
and only if , or for some nonempty
subset of , where is the quasi
conjunction of the conditional events in . Then, we examine the
inference rules , , , and of System~P
and other well known inference rules ( , ,
). We also show that , where
is the conjunction of the conditional events in
. We characterize p-entailment by showing that
p-entails if and only if .
Finally, we examine \emph{Denial of the antecedent} and \emph{Affirmation of
the consequent}, where the p-entailment of from does
not hold, by showing that $(E_3|H_3)|\mathcal{C}(\mathcal{F})\neq1.
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
Forgetting complex propositions
This paper uses possible-world semantics to model the changes that may occur
in an agent's knowledge as she loses information. This builds on previous work
in which the agent may forget the truth-value of an atomic proposition, to a
more general case where she may forget the truth-value of a propositional
formula. The generalization poses some challenges, since in order to forget
whether a complex proposition is the case, the agent must also lose
information about the propositional atoms that appear in it, and there is no
unambiguous way to go about this.
We resolve this situation by considering expressions of the form
, which quantify over all possible (but
minimal) ways of forgetting whether . Propositional atoms are modified
non-deterministically, although uniformly, in all possible worlds. We then
represent this within action model logic in order to give a sound and complete
axiomatization for a logic with knowledge and forgetting. Finally, some
variants are discussed, such as when an agent forgets (rather than
forgets whether ) and when the modification of atomic facts is done
non-uniformly throughout the model
From Logic Programming to Human Reasoning:: How to be Artificially Human
Results of psychological experiments have shown that humans make assumptions, which are not necessarily valid, that they are influenced by their background knowledge and that they reason non-monotonically. These observations show that classical logic does not seem to be adequate for modeling human reasoning. Instead of assuming that humans do not reason logically at all, we take the view that humans do not reason classical logically. Our goal is to model episodes of human reasoning and for this purpose we investigate the so-called Weak Completion Semantics. The Weak Completion Semantics is a Logic Programming approach and considers the least model of the weak completion of logic programs under the three-valued Łukasiewicz logic.
As the Weak Completion Semantics is relatively new and has not yet been extensively investigated, we first motivate why this approach is interesting for modeling human reasoning. After that, we show the formal correspondence to the already established Stable Model Semantics and Well-founded Semantics. Next, we present an extension with an additional context operator, that allows us to express negation as failure. Finally, we propose a contextual abductive reasoning approach, in which the context of observations is relevant. Some properties do not hold anymore under this extension. Besides discussing the well-known psychological experiments Byrne’s suppression task and Wason’s selection task, we investigate an experiment in spatial reasoning, an experiment in syllogistic reasoning and an experiment that examines the belief-bias effect. We show that the results of these experiments can be adequately modeled under the Weak Completion Semantics. A result which stands out here, is the outcome of modeling the syllogistic reasoning experiment, as we have a higher prediction match with the participants’ answers than any of twelve current cognitive theories.
We present an abstract evaluation system for conditionals and discuss well-known examples from the literature. We show that in this system, conditionals can be evaluated in various ways and we put up the hypothesis that humans use a particular evaluation strategy, namely that they prefer abduction to revision. We also discuss how relevance plays a role in the evaluation process of conditionals. For this purpose we propose a semantic definition of relevance and justify why this is preferable to a exclusively syntactic definition. Finally, we show that our system is more general than another system, which has recently been presented in the literature.
Altogether, this thesis shows one possible path on bridging the gap between Cognitive Science and Computational Logic. We investigated findings from psychological experiments and modeled their results within one formal approach, the Weak Completion Semantics. Furthermore, we proposed a general evaluation system for conditionals, for which we suggest a specific evaluation strategy. Yet, the outcome cannot be seen as the ultimate solution but delivers a starting point for new open questions in both areas
Rethinking the Acceptability and Probability of Indicative Conditionals
The chapter is devoted to the probability and acceptability of indicative conditionals. Focusing on three influential theses, the Equation, Adams’ thesis, and the qualitative version of Adams’ thesis, Sikorski argues that none of them is well supported by the available empirical evidence. In the most controversial case of the Equation, the results of many studies which support it are, at least to some degree, undermined by some recent experimental findings. Sikorski discusses the Ramsey Test, and Lewis’s triviality proof, with special attention dedicated to the popular ways of blocking it. Sikorski concludes that the role of the three theses in future studies of conditionals should be re-thought, and he presents alternative proposals
Belief Dynamics: (Epistemo)logical Investigations
C.S. Peirce's and Isaac Levi's accounts of the belief-doubt-belief model are discussed and evaluated. It is argued that the contemporary study of belief change has metamorphosed into a branch of philosophical logic where empirical considerations have become obsolete. A case is made for reformulations of belief change systems that do allow for empirical tests. Last, a belief change system is presented that (1) uses finite representations of information, (2) can adequately deal with inconsistencies, (3) has finite operations of change, (4) can do without extra-logical elements, and (5) only licenses consistent beliefs
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