A Solution to the Surprise Exam Paradox in Constructive Mathematics

Ardeshir, Mohammad; Ramezanian, Rasoul

doi:10.1017/s1755020312000160

Cited by 4 publications

(5 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For example, Gerbrandy sees the puzzle in the assumption that announcements are in general successful [5], and Baltag, to solve the paradox, lets the students to revise their trust to the teacher once they reach the paradox [7]. In [1], the paradox is investigated in a constructive view, considering free will of the teacher. In this paper, we claim that the puzzle in SEP is that students (wrongly) assume the day that teacher is going to take the exam is predetermined!…”

Section: The Surprise Exam Paradoxmentioning

confidence: 99%

See 1 more Smart Citation

A Constructive Epistemic Logic with Public Announcement (Non-Predetermined Possibilities)

Ramezanian

2013

Preprint

Self Cite

View full text Add to dashboard Cite

We argue that the notion of epistemic possible worlds in constructivism (intuitionism) is not as the same as it is in classic view, and there are possibilities, called non-predetermined worlds, which are ignored in (classic) Epistemic Logic. Regarding non-predetermined possibilities, we propose a constructive epistemic logic and prove soundness and completeness theorems for it. We extend the proposed logic by adding a public announcement operator. To declare the significance of our work, we formulate the well-known Surprise Exam Paradox, SEP, via the proposed constructive epistemic logic and then put forward a solution for the paradox. We clarify that the puzzle in the SEP is because of students'(wrong) assumption that the day of the exam is necessarily predetermined.

show abstract

Section: The Surprise Exam Paradoxmentioning

confidence: 99%

“…The surprise exam paradox, SEP (see [8,9,10]), was formulated via classic epistemic logic in different ways [2,9,11,13]. Also the paradox was formulated in constructive analysis [1]. In section 3, we formally model SEP in the proposed constructive epistemic logic.…”

mentioning

confidence: 99%

A Constructive Epistemic Logic with Public Announcement (Non-Predetermined Possibilities)

Ramezanian

2013

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…In this section, inspired by Brouwer's choice sequences, we introduce persistently evolutionary Turing machines. A persistently evolutionary Turing machine is a machine that its inner structure during its computation on any input may evolve 4 . But this evolution is in the way that if a computist does not have access to the inner structure of the machine then he cannot recognize whether the machine evolves or not.…”

Section: Persistently Evolutionary Turing Machinesmentioning

confidence: 99%

“…Readers may see[4], where the notion of the free will is used to settle the well-known Surprise Exam Paradox. The notion of the free will is also discussed in author's PhD thesis[26], and in[3] 6.…”

mentioning

confidence: 99%

Computation Environments, An Interactive Semantics for Turing Machines (which P is not equal to NP considering it)

Ramezanian

2012

Preprint

Self Cite

View full text Add to dashboard Cite

To scrutinize notions of computation and time complexity, we introduce and formally define an interactive model for computation that we call it the computation environment. A computation environment consists of two main parts: i) a universal processor and ii) a computist who uses the computability power of the universal processor to perform effective procedures. The notion of computation finds it meaning, for the computist, through his interaction with the universal processor. We are interested in those computation environments which can be considered as alternative for the real computation environment that the human being is its computist. These computation environments must have two properties: 1-being physically plausible, and 2-being enough powerful. Based on Copeland' criteria for effective procedures, we define what a physically plausible computation environment is. By being enough powerful, we mean that the universal processor of the computation environment, must be in a way that the computist can carry out (via the universal processor) all logical deductions that the human being can carry out. We construct two physically plausible and enough powerful computation environments: 1-the Turing computation environment, denoted by E T , and 2-a persistently evolutionary computation environment, denoted by E e , which persistently evolve in the course of executing the computations. We prove that the equality of complexity classes P and NP in the computation environment E e conflicts with the free will of the computist. We provide an axiomatic system T for Turing computability and prove that ignoring just one of the axiom of T , it would not be possible to derive P = NP from the rest of axioms. We prove that the computist who lives inside the environment E T , can never be confident that whether he lives in a static environment or a persistently evolutionary one.

show abstract

“…2 This is, to the best of our knowledge, the first application of intuitionistic mathematics in the social sciences, but there have been applications in computer science and some discussions in operations research; see for example McAloon and Tretkoff (1997). A clever application of Brouwer's continuity principle in a finite horizon game (the surprise exam paradox) is in Ardeshir and Ramezanian (2012), who represent information about the game in an infinite sequence with a subfinite, but constructively not necessarily finite, number of changes in the sequence's terms. approaches to valuation are intuitionistically quite different and that only the earnings approach satisfies Brouwer's continuity principle.…”

Section: Introductionmentioning

confidence: 99%

Using Brouwer’s continuity principle to pick stocks

Stecher

Atten²

2013

Ann Oper Res

View full text Add to dashboard Cite

This article shows that an apparent puzzle in finance and accounting is resolved by changing from classical to constructive (more specifically, intuitionistic) mathematics. Our position is that it is unproblematic if real-world actors behave inconsistently with nonconstructive mathematical results. Thus the solution to our puzzle lies in a deeper challenge to the standard view of how rational agents reason. The alternative we propose gives refutable predictions that find support in the empirical capital markets literature. Our main tool, intuitionistic mathematics, plays a similar role in the mathematical philosophy literature to that of ambiguity in decision theoretic work.

show abstract

A Solution to the Surprise Exam Paradox in Constructive Mathematics

Cited by 4 publications

References 16 publications

A Constructive Epistemic Logic with Public Announcement (Non-Predetermined Possibilities)

A Constructive Epistemic Logic with Public Announcement (Non-Predetermined Possibilities)

Computation Environments, An Interactive Semantics for Turing Machines (which P is not equal to NP considering it)

Using Brouwer’s continuity principle to pick stocks

Contact Info

Product

Resources

About