Related papers: How long is a Proof? - A short note
Incongruity often makes people laugh. You have to be smart to say stupid things. It requires to be even smarter for understanding them. This paper is a shameless attempt to formalize this intelligent behavior in the case of an agent…
It has been argued that reduction procedures are closely connected to the question about identity of proofs and that accepting certain reductions would lead to a trivialization of identity of proofs in the sense that every derivation of the…
This very short correction notes a gap in an argument of an earlier paper, and also provides a theorem of similar flavor to the main result of that paper.
In program semantics and verification, reasoning about loops is complicated by the need to produce two separate mathematical arguments: an invariant, for functional properties (ignoring termination); and a variant, for termination (ignoring…
A little general abstract combinatorial nonsense delivered in this note is a presentation of some old and basic concepts, central to discrete mathematics, in terms of new words. The treatment is from a structural and systematic point of…
A short proof is given that the graphs with proper interval representations are the same as the graphs with unit interval representations.
In introductions to the subject for a general audience of mathematicians or logicians, the univalence axiom is typically explained by handwaving. This gives rise to several misconceptions, which cannot be properly addressed in the absence…
We investigate the variance of the length of the longest common subsequences of two independent random words of size $n$, where the letters of one word are i.i.d. uniformly drawn from $\{\alpha_1, \alpha_2, \cdots, \alpha_m\}$, while the…
Independence -- the study of what is relevant to a given problem of reasoning -- has received an increasing attention from the AI community. In this paper, we consider two basic forms of independence, namely, a syntactic one and a semantic…
This paper has been temporarily withdrawn, pending a revised version taking into account similarities between this paper and the recent work of del Barrio, Gine and Utzet (Bernoulli, 11 (1), 2005, 131-189).
This paper has been withdrawn
Practicing mathematicians often assume that mathematical claims, when they are true, have good reasons to be true. Such a state of affairs is "unreasonable", in Wigner's sense, because basic results in computational complexity suggest that…
We obtain simple proofs of certain inequalites for bivariate means.
Existing self-explaining models typically favor extracting the shortest possible rationales - snippets of an input text "responsible for" corresponding output - to explain the model prediction, with the assumption that shorter rationales…
It is well known that the resolution method (for propositional logic) is complete. However, completeness proofs found in the literature use an argument by contradiction showing that if a set of clauses is unsatisfiable, then it must have a…
This paper has been withdrawn by the authors
Standard proofs of Lusin's theorem, using simple functions, are sometimes quite elaborate. Here, we give a one-sentence proof of Lusin's theorem. We do not believe our approach, by way of inverse images, is new. However, this particular…
A critical review is presented on the most recent attempt to generally explain the notion of "statistical symmetry". This particular explanation, however, is incomplete and misses one important and essential aspect. The aim of this short…
This paper has been withdrawn by the authors due to an error in Section 7.
Consider the following story: A teacher announces to her students a test for the following week, such that the test will be ``surprising''. The students use this as the basis for a ``logical derivation'' and reach a contradiction, which…