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Ideas from 'Non-Monotonic Logic' by G. Aldo Antonelli [2014], by Theme Structure

[found in 'Stanford Online Encyclopaedia of Philosophy' (ed/tr Stanford University) [plato.stanford.edu ,-]].

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2. Reason / E. Argument / 1. Argument
19115 You can 'rebut' an argument's conclusion, or 'undercut' its premises
                        Full Idea: A 'rebut' of an argument establishes that its conclusion is not the case. An 'undercut' of the argument shows that the premises do not support that conclusion.
                        From: G. Aldo Antonelli (Non-Monotonic Logic [2014], 3.2)
4. Formal Logic / E. Nonclassical Logics / 1. Nonclassical Logics
19119 We infer that other objects are like some exceptional object, if they share some of its properties
                        Full Idea: The exceptional status of an object with respect to some default is more likely to spread to other objects if they share properties with that object that may play a role in explaining the exceptional status.
                        From: G. Aldo Antonelli (Non-Monotonic Logic [2014], 4)
                        A reaction: This is an example of the sort of rational behaviour we exhibit, and which a 'real life' logic would somehow need to capture. I would suggest the essentialist logic designed by Kit Fine as a first port of call.
4. Formal Logic / E. Nonclassical Logics / 12. Non-Monotonic Logic
19111 Reasoning may be defeated by new premises, or by finding out more about the given ones
                        Full Idea: Most defeasible reasoning is externally dynamic, affected by the addition of further premises. But there is also an internal (or 'diachronic') dynamic, when further analysis reveals more about the given premises.
                        From: G. Aldo Antonelli (Non-Monotonic Logic [2014], 1)
19113 Weakest Link Principle: prefer the argument whose weakest link is the stronger
                        Full Idea: In the Weakest Link Principle, an argument is preferred to another conflicting argument if its weakest defeasible link is stronger than the weakest defeasible link in the conflicting argument.
                        From: G. Aldo Antonelli (Non-Monotonic Logic [2014], 2.1)
                        A reaction: [He cites John Pollock 1991] This sounds like the elementary principle applied when choosing a rope by which to hang a large weight above your head. It gets non-monotonic logic off the ground - if you know how to evaluate 'weakest'.
19114 Should we accept Floating Conclusions, derived from two arguments in conflict?
                        Full Idea: There is much discussion of whether Floating Conclusions should be derived, given that they were derived from two arguments which conflict with one another.
                        From: G. Aldo Antonelli (Non-Monotonic Logic [2014], 2.3)
19116 Non-monotonic core: Reflexivity, Cut, Cautious Monotonicity, Left Logical Equivalence, Right Weakening
                        Full Idea: Conservative core of non-monotonic logic:Reflexivity (p proves p), Cut (if p proves q, it proves their joint implications), Cautious Monotonicity, Left Logical Equivalence (equivalences have same consequences), Right Weakening (non-m preserves classical).
                        From: G. Aldo Antonelli (Non-Monotonic Logic [2014], 3.5.1)
                        A reaction: [Highly compressed, and without symbols]
19117 We can rank a formula by the level of surprise if it were to hold
                        Full Idea: We can think of an 'ordinal ranking function' κ([φ)] as the level of surprise we would face were φ to hold, up to maximal surprise.
                        From: G. Aldo Antonelli (Non-Monotonic Logic [2014], 3.5.2)
                        A reaction: This suggests that Bayes's Theorem might be relevant to non-monotonic logic. This suggests that registering surprise would need to be an important feature of robot behaviour.
19118 People don't actually use classical logic, but may actually use non-monotonic logic
                        Full Idea: Test subjects seem to perform very poorly in various reasoning tests (Wason Selection, Suppression Task), suggesting logic has a subordinate role, but this may be using classical logic, where non-monotonic logics would be more appropriate.
                        From: G. Aldo Antonelli (Non-Monotonic Logic [2014], 4)
                        A reaction: Fred Sommers presents his Term Logic (based on Aristotle) as closer to how people actually reason. It is certainly crazy to infer that most people's everyday reasoning is irrational. Induction is highly rational; it's just not deductive.
5. Theory of Logic / K. Features of Logics / 10. Monotonicity
19110 In classical logic the relation |= has Monotony built into its definition
                        Full Idea: In classical logic, Monotony follows immediately from the nature of the relation |=, for Γ |= φ holds precisely when φ is true on every interpretation on which all sentences in Γ are true.
                        From: G. Aldo Antonelli (Non-Monotonic Logic [2014], 1)
                        A reaction: That is, semantic consequence (|=) is defined in terms of a sentence (φ) always being true if some other bunch of sentences (Γ) are true. Hence the addition of further sentences to Γ will make no difference - which is Monotony.
19112 Cautious Monotony ignores proved additions; Rational Monotony fails if the addition's negation is proved
                        Full Idea: Basic Monotony: something stays proved if further premises are added. Cautious Monotony: the addition of something which has been proved makes no difference. Rational Monotony: it stays proved as long as the addition's negation hasn't been proved.
                        From: G. Aldo Antonelli (Non-Monotonic Logic [2014], 1)
                        A reaction: [A compressed and non-symbolic summary]