Vårterminen 2009
- 6/2: Claes Strannegård Reasoning Processes in Propositional Logic A computer-based experiment was conducted in which eight participants were asked to determine whether 80 randomly generated formulas of propositional logic were tautologies. The participants were all male in the age span 23-43 years and all of them had undergone training in propositional logic at university level. In each trial a propositional formula was presented to the participant. A time-limit of 45 seconds applied to each trial and no aids were allowed. For each trial, two aggregated psychological measures of difficulty were used: (i) the proportion of the participants who answered the trial correctly, and (ii) the average response time among the participants who gave correct answers. To model these psychological measures a cognitive architecture for propositional reasoning is defined. The cognitive resources are modeled according to the memory model of Atkinson and Shiffrin and features declarative memory, sensory memory, working memory, and procedural memory. Propositional reasoning is modeled on the basis of the state transition model of Newell and Simon. Specific proof systems for showing validity and non-validity with limited cognitive resources are defined. Our results indicate that the length of the shortest proofs in these proof systems is a substantially better predictor of both of the above psychological measures than is formula length.
- 27/2: INSTÄLLT
- 6/3: Jens Allwood Feedback, coactivation and coconstruction in dialog
- 20/3: Jörgen Sjögren Explications, Abstract Objects, and Structuralism
- 27/3: Fredrik Engström Logiska operatorer i Dependence logic Jag kommer presentera ett förslag till ett allmänt ramverk för semantik av (logiska) operatorer i "Dependence Logic" (DL). Arbetet är pågående och de få resultat som kommer presenteras är som mest preliminära. Syftet är att ramverket sedan skall användas för en invariansanalys av (logiska) operatorer i DL. Ingen kunskap om DL förutsetts.
- 17/4: Denis Bonnay Definability and invariance in infinitary logic without equality I will present some strengthening of the connection between infinitary languages and invariance criteria for logical operations, as a generalization of an (old) result by Marc Krasner on definability in infinitary logic and groups of automorphisms. Krasner showed that, given a set M, there is a one-one correspondence between sets of operations on M which are closed under definability in L_{\infty,\infty} and groups of permutations on M. Independently, Solomon Feferman asked in which logical language operations invariant under strong homomorphisms were definable (I will define precisely what a strong homomorphism is). I show that Feferman's question can be answered by generalizing Krasner's theorem, so as to get a one-one correspondence between sets of operations closed under definability in L_{\infty,\infty} without equality and monoids of homomorphisms.
- 24/4: Thierry Coquand An introduction to constructive mathematics After a description of the historical background I will try to explain how constructive mathematics is thought of by constructive mathematicians (Bridges, Lombardi, Richman, ...) as mathematics developed using intuitionistic logic. I will then try to survey some works in constructive algebra and analysis.
- 15/5: Anton Hedin Formell Topologi, Generaliserade Reella Tal, och Intervall-analys Jag kommer att ge en kort introduktion till formell topologi, vilket är en konstruktiv (och predikativ) presentation av Locale-teori, mer känt som punktfri topologi. Som ett exempel kommer vi se hur de reella talen R definieras som ett formellt rum. Genom att använda en typ av kompaktifiering kan man bädda in R i en utvidgning R_p som, förutom de reella talen, bland annat innehåller representationer av slutna intervall [a,b] (a,b reella tal). Vi kommer också att se ett utvidgningsresultat för kontinuerliga funktioner vilket öppnar för möjligheten att använda R_p som en domän för intervall-analys.
- (29/5: Göran Sundholm Making sense of truth-values; Frege in mysterious circumstances Göran Sundholm kommer att hålla ett föredrag på datavetenskap på Chalmers. Tid 10:15 i EDIT-huset, sal ES51.)
- 5/6: Martin Kaså Palmé (OBS Nytt datum!) Experimental logics, mechanism and knowable consistency På detta arbetsseminarium vill jag ventilera och förbättra en av mina aktuella texter - ett (bitvis skissartat) utkast till en kort logisk-filosofisk artikel inom mitt avhandlingsområde. Som antyds av den preliminära titeln (rubriken ovan) anknyter det till den s.k. "Lucas-Penrose-tesen" (grovt sett: att Gödels (2:a) ofullständighetssats visar att det mänskliga medvetandet inte kan vara "mekaniskt" eller "algoritmiskt"). Dessa "gödelianska" argument är tämligen väl genomtröskade (och har övertygat mycket få) men här har vi en ny twist: jag kommenterar vilket eventuellt värde Jeroslows experimentella logiker kan ha för att kasta ljus över frågan - en tanke som finns hos Allen Hazen och Stewart Shapiro.