Introduction: Algorithmic Thought

Towards Algorithmic Cut-Introduction

We describe a method for abbreviating an analytic proof in classical first-order logic by the introduction of a lemma. Our algorithm is based on first computing a compressed representation of the terms present in the analytic proof and then a cut-formula that realizes such a compression. This method can be applied to the output of automated theorem provers, which typically produce analytic proofs.

Algorithmic introduction of quantified cuts

We describe a method for inverting Gentzen’s cut-elimination in classical first-order logic. Our algorithm is based on first computing a compressed representation of the terms present in the cut-free proof and then cut-formulas that realize such a compression. Finally, a proof using these cut-formulas is constructed. This method allows an exponential compression of proof length. It can be appli...

An Introduction to Morteza Motahari''''s Political Thought

Although Motahari is not a political thinker but analyzing his political ideas and believes amongst the ideas of Iranian political thinkers in the last 5 decades is indeed essential because Motahari’s political standpoint has a key role in Islamic revolution of Iran. This paper regards Motahari''s vision to his time and studies his writings according to the questions he faced and posed in his t...

Introduction: the cognitive neuroscience of thought.

Human thought has been a puzzling subject among philosophers for the major part of our recorded history, most famously encapsulated in Descartes' Cogito ergo sum (I think therefore I am). Although our knowledge of thought and its benefits has come a long way since Descartes, it is only in recent times that empirical investigations into theneuroscientific bases of thought and cognition have been...

Thought, Language, and Ontology: An Introduction