David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Journal of Logic, Language and Information 19 (3):283-314 (2010)
We conducted a computer-based psychological experiment in which a random mix of 40 tautologies and 40 non-tautologies were presented to the participants, who were asked to determine which ones of the formulas were tautologies. The participants were eight university students in computer science who had received tuition in propositional logic. The formulas appeared one by one, a time-limit of 45 s applied to each formula and no aids were allowed. For each formula we recorded the proportion of the participants who classified the formula correctly before timeout and the mean response time among those participants. We propose a new proof formalism for modeling propositional reasoning with bounded cognitive resources. It models declarative memory, visual memory, working memory, and procedural memory according to the memory model of Atkinson and Shiffrin and reasoning processes according to the model of Newell and Simon. We also define two particular proof systems, T and NT, for showing propositional formulas to be tautologies and non-tautologies, respectively. The accuracy was found to be higher for non-tautologies than for tautologies ( p T was.89 and for non-tautologies the correlation between latency and minimum proof length in NT was.87
|Keywords||Bounded resources Proof system Propositional logic Psychological experiment Reasoning|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
Nelson Cowan (2001). The Magical Number 4 in Short-Term Memory: A Reconsideration of Mental Storage Capacity. Behavioral and Brain Sciences 24 (1):87-114.
A. S. Troelstra (2000). Basic Proof Theory. Cambridge University Press.
Philip Johnson-Laird (2006). How We Reason. OUP Oxford.
Sara Negri & Jan von Plato (2001). Structural Proof Theory. Cambridge University Press.
Citations of this work BETA
Claes Strannegård, Fredrik Engström, Abdul Rahim Nizamani & Lance Rips (2013). Reasoning About Truth in First-Order Logic. Journal of Logic, Language and Information 22 (1):115-137.
Similar books and articles
Achille C. Varzi (1992). Complementary Logics for Classical Propositional Languages. Kriterion: Journal of Philosophy 4 (1):20-24.
Juan A. Garc (2007). Mental Models in Propositional Reasoning and Working Memory's Central Executive. Thinking and Reasoning 13 (4):370 – 393.
Jan Krajíček (2004). Dual Weak Pigeonhole Principle, Pseudo-Surjective Functions, and Provability of Circuit Lower Bounds. Journal of Symbolic Logic 69 (1):265 - 286.
Jan Krajíček (1995). Bounded Arithmetic, Propositional Logic, and Complexity Theory. Cambridge University Press.
Nathan Segerlind (2007). The Complexity of Propositional Proofs. Bulletin of Symbolic Logic 13 (4):417-481.
M. G. Beavers (1994). Theorem Counting. Topoi 13 (1):61-65.
Pavel Hrubeš (2007). Lower Bounds for Modal Logics. Journal of Symbolic Logic 72 (3):941 - 958.
Added to index2009-10-14
Total downloads44 ( #92,526 of 1,793,158 )
Recent downloads (6 months)5 ( #169,309 of 1,793,158 )
How can I increase my downloads?