75,643 research outputs found
On Dialetheic Entailment
The entailment connective is introduced by Priest (2006b). It aims to capture, in a dialetheically acceptable way, the informal notion of logical consequence. This connective does not “fall foul” of Curry’s Paradox by invalidating an inference rule called “Absorption” (or “Contraction”) and the classical logical theorem called “Assertion”. In this paper we show that the semantics of entailment, given by Priest in terms of possible worlds, is inadequate. In particular, we will argue that Priest’s counterexamples to Absorption and Assertion use in the metalanguage a dialetheically unacceptable principle. Furthermore, we show that the rejection of Assertion undermines Priest’s claim that the entailment connective expresses the notion of logical consequence
Putting time into proof outlines
A logic for reasoning about timing of concurrent programs is presented. The logic is based on proof outlines and can handle maximal parallelism as well as resource-constrained execution environments. The correctness proof for a mutual exclusion protocol that uses execution timings in a subtle way illustrates the logic in action
Rejection in Łukasiewicz's and Słupecki's Sense
The idea of rejection originated by Aristotle. The notion of rejection
was introduced into formal logic by Łukasiewicz [20]. He applied it to
complete syntactic characterization of deductive systems using an axiomatic
method of rejection of propositions [22, 23]. The paper gives not only genesis,
but also development and generalization of the notion of rejection. It also
emphasizes the methodological approach to biaspectual axiomatic method of
characterization of deductive systems as acceptance (asserted) systems and
rejection (refutation) systems, introduced by Łukasiewicz and developed by
his student Słupecki, the pioneers of the method, which becomes relevant in
modern approaches to logic
A Meta-Logic of Inference Rules: Syntax
This work was intended to be an attempt to introduce the meta-language for
working with multiple-conclusion inference rules that admit asserted
propositions along with the rejected propositions. The presence of rejected
propositions, and especially the presence of the rule of reverse substitution,
requires certain change the definition of structurality
Inferring Acceptance and Rejection in Dialogue by Default Rules of Inference
This paper discusses the processes by which conversants in a dialogue can
infer whether their assertions and proposals have been accepted or rejected by
their conversational partners. It expands on previous work by showing that
logical consistency is a necessary indicator of acceptance, but that it is not
sufficient, and that logical inconsistency is sufficient as an indicator of
rejection, but it is not necessary. I show how conversants can use information
structure and prosody as well as logical reasoning in distinguishing between
acceptances and logically consistent rejections, and relate this work to
previous work on implicature and default reasoning by introducing three new
classes of rejection: {\sc implicature rejections}, {\sc epistemic rejections}
and {\sc deliberation rejections}. I show how these rejections are inferred as
a result of default inferences, which, by other analyses, would have been
blocked by the context. In order to account for these facts, I propose a model
of the common ground that allows these default inferences to go through, and
show how the model, originally proposed to account for the various forms of
acceptance, can also model all types of rejection.Comment: 37 pages, uses fullpage, lingmacros, name
The Epistemic Significance of Valid Inference – A Model-Theoretic Approach
The problem analysed in this paper is whether we can gain knowledge by using valid inferences, and how we can explain this process from a model-theoretic perspective. According to the paradox of inference (Cohen & Nagel 1936/1998, 173), it is logically impossible for an inference to be both valid and its conclusion to possess novelty with respect to the premises. I argue in this paper that valid inference has an epistemic significance, i.e., it can be used by an agent to enlarge his knowledge, and
this significance can be accounted in model-theoretic terms. I will argue first that the paradox is based on an equivocation, namely, it arises because logical containment, i.e., logical implication, is identified with epistemological containment, i.e., the knowledge of the premises entails the knowledge of the conclusion. Second, I will argue that a truth-conditional theory of meaning has the necessary resources to explain the epistemic significance of valid inferences. I will explain this epistemic significance starting from Carnap’s semantic theory of meaning and Tarski’s notion of satisfaction. In this way I will counter (Prawitz 2012b)’s claim that a truth-conditional theory of meaning is not able to account the legitimacy of valid inferences, i.e., their epistemic significance
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