On the weak intuitionistic fuzzy implication based on △ operation

In this paper, a new weak intuitionistic fuzzy implication is introduced. Fulfillment of some axioms and properties, together with the Modus Ponens and Modus Tollens inference rules are investigated. Negation induced by the newly proposed implication is presented.

On Basic Probability Logic Inequalities

We give some simple examples of applying some of the well-known elementary probability theory inequalities and properties in the field of logical argumentation. A probabilistic version of the hypothetical syllogism inference rule is as follows: if propositions A, B, C, A→B, and B→C have probabilities a, b, c, r, and s, respectively, then for probability p of A→C, we have f(a,b,c,r,s)≤p≤g(a,b,c,r,s), for some functions f and g of given parameters. In this paper, after a short overview of known rules related to conjunction and disjunction, we proposed some probabilized forms of the hypothetical syllogism inference rule, with the best possible bounds for the probability of conclusion, covering simultaneously the probabilistic versions of both modus ponens and modus tollens rules, as already considered by Suppes, Hailperin, and Wagner.

Selective Scientific Realism and Truth-Transfer in Theories of Molecular Structure

This chapter examines theoretical advances in understanding molecular structures at the turn of the 20th century which resulted from the Blomstrand-Jørgensen/Werner debate about the structure of cobalt complexes. Both models made predictions testable through precipitation experiments, which eventually led to Werner’s model replacing the Blomstrand-Jørgensen model of cobalt complexes. We argue that this example of theory change fits within a selective scientific realist framework: namely, the factors which gave rise to the predictive success of the failed model survived in the theory that replaced it. We further argue that the lessons from this historical case can illuminate how two contemporary objections to realism—P. Kyle Stanford’s Problem of Unconceived Alternatives and Timothy D. Lyons’ pessimistic modus tollens argument—fall short as arguments against realism.

Logical Intuition Is Not Really About Logic

Recent research suggest that reasoners are able to draw simple logical or probabilistic inferences relatively intuitively and automatically, a capacity which has been termed “logical intuition” (see, for example, De Neys & Pennycook, 2019). A key finding in support of this interpretation is that conclusion validity consistently interferes with judgments of conclusion believability, suggesting that information about logical validity is available quickly enough to interfere with belief judgments. In this paper we examined whether logical intuitions arise because reasoners are sensitive to the logical features of problem or another structural feature that just happens to aligns with logical validity. In three experiments (N = 113, 137, and 122), we presented participants with logical (determinate) and pseudo-logical (indeterminate) arguments and asked them to judge the validity or believability of the conclusion. Logical arguments had determinately valid or invalid conclusions, whereas pseudo-logical arguments were all logically indeterminate, but some were pseudo-valid (possible ‘strong’ arguments) and others pseudo-invalid (possible ‘weak’ arguments). Experiments 1 and 2 used simple Modus Ponens and Affirming the Consequent structures; Experiment 3 used more complex Denying the Antecedent and Modus Tollens structures. In all three experiments, we found that pseudo-validity interfered with belief judgments to the same extent as real validity. Altogether, these findings suggest that whilst people are able to draw inferences intuitively, and these inferences impact on belief judgments, they are not ‘logical intuitions.’ Rather, the intuitive inferences are driven by the processing of more superficial structural features that happen to align with logical validity.

A Fuzzy Take on the Logical Issues of Statistical Hypothesis Testing

Statistical Hypothesis Testing (SHT) is a class of inference methods whereby one makes use of empirical data to test a hypothesis and often emit a judgment about whether to reject it or not. In this paper, we focus on the logical aspect of this strategy, which is largely independent of the adopted school of thought, at least within the various frequentist approaches. We identify SHT as taking the form of an unsound argument from Modus Tollens in classical logic, and, in order to rescue SHT from this difficulty, we propose that it can instead be grounded in t-norm based fuzzy logics. We reformulate the frequentists’ SHT logic by making use of a fuzzy extension of Modus Tollens to develop a model of truth valuation for its premises. Importantly, we show that it is possible to preserve the soundness of Modus Tollens by exploring the various conventions involved with constructing fuzzy negations and fuzzy implications (namely, the S and R conventions). We find that under the S convention, it is possible to conduct the Modus Tollens inference argument using Zadeh’s compositional extension and any possible t-norm. Under the R convention we find that this is not necessarily the case, but that by mixing R-implication with S-negation we can salvage the product t-norm, for example. In conclusion, we have shown that fuzzy logic is a legitimate framework to discuss and address the difficulties plaguing frequentist interpretations of SHT.

Content, Context, and Logic

Non-propositionalism has additionally been fueled by the fact that modals and conditionals seem to give raise to failure of classical patterns of inference, for instance, modus ponens and modus tollens. Since non-propositionalist accounts typically invalidate some of these patterns of inference, the apparent counterexamples have been taken as further data in support of such treatments. This chapter argues that this is a mistaken reaction to the apparent counterexamples. The seeming violations of classical patterns of inference yet again result from a faulty assumption of the extra-linguistic account of context-sensitivity resolution, and a failure to account for the effects of discourse conventions on the interpretation of modal discourse. The chapter’s account of modality, which treats them as prominence-sensitive expressions whose interpretation is determined by discourse conventions, predicts and explains the apparent counterexamples, while nevertheless preserving classical logic.

Aturan penarikan kesimpulan

Beberapa penarikan kesimpulan yang sahih atau valid yang akan dibahas pada bagian ini,di antaranya adalah modus ponens, modus tolens, dan silogisme. Modus ponens, modus tollens dan silogisme adalah metode atau cara yang digunakan dalam penarikan kesimpulan. Proses penarikan kesimpulan terdiri atas beberapa pernyataan yang diketahui nilai kebenarannya (disebut premis). Kemudian dengan menggunakan prinsipprinsip logika dapat diturunkan pernyataan baru (disebut kesimpulan/konklusi) yang diturunkan dari premispremis semula.

Fuzzy Reasoning Method Based on Distance Measure and Its Reductive Property

This paper shows a basic and original fuzzy reasoning method that can draw a novel study direction of the approximate inference in fuzzy systems with uncertainty. Firstly we propose a criterion function for checking of the reductive property about fuzzy modus ponens (FMP) and fuzzy modus tollens (FMT). Secondly unlike fuzzy reasoning methods based on the similarity measure, we propose a principle of new fuzzy reasoning method based on distance measure and then present two theorems for FMP and FMT. Thirdly through the several computational experiments, we show that proposed method is simple and effective, and in accordance with human thinking. Finally we pointed out conclusion that proposed method does satisfy the convergence of the fuzzy control and has not information loss.

Is Conspiracy Theorizing Really Epistemically Problematic?

In an article based on a recent address to the Royal Institute of Philosophy, Keith Harris has argued that there is something epistemically wrong with conspiracy theorizing. Although he finds “standard criticisms” of conspiracy theories wanting, he argues that there are three subtle but significant problems with conspiracy theorizing: (1) It relies on an invalid probabilistic version of modus tollens. (2) It involves a problematic combination of both epistemic virtues and vices. And (3) it lacks an adequate basis for trust in its information sources. In response to Harris, this article argues that, like previous criticisms, these criticisms do little to undermine conspiracy theorizing as such. And they do not give us good reasons to dismiss any particular conspiracy theory without consideration of the relevant evidence.