Logical gaps in the approximate solutions of the social learning game and an exact solution

After the social learning models were proposed, finding the solutions of the games becomes a well-defined mathematical question. However, almost all papers on the games and their applications are based on solutions built upon either an add-hoc argument or a twisted Bayesian analysis of the games. Here, we present logical gaps in those solutions and an exact solution of our own. We also introduced a minor extension to the original game such that not only logical difference but also difference in action outcomes among those solutions become visible.Comment: A major revisio

Eigenlogic: a Quantum View for Multiple-Valued and Fuzzy Systems

We propose a matrix model for two- and many-valued logic using families of observables in Hilbert space, the eigenvalues give the truth values of logical propositions where the atomic input proposition cases are represented by the respective eigenvectors. For binary logic using the truth values {0,1} logical observables are pairwise commuting projectors. For the truth values {+1,-1} the operator system is formally equivalent to that of a composite spin 1/2 system, the logical observables being isometries belonging to the Pauli group. Also in this approach fuzzy logic arises naturally when considering non-eigenvectors. The fuzzy membership function is obtained by the quantum mean value of the logical projector observable and turns out to be a probability measure in agreement with recent quantum cognition models. The analogy of many-valued logic with quantum angular momentum is then established. Logical observables for three-value logic are formulated as functions of the Lz observable of the orbital angular momentum l=1. The representative 3-valued 2-argument logical observables for the Min and Max connectives are explicitly obtained.Comment: 11 pages, 2 table

Towards modelling dialectic and eristic argumentation on the social web

Modelling arguments on the social web is a key challenge for those studying computational argumentation. This is because formal models of argumentation tend to assume dialectic and logical argument, whereas argumentation on the social web is highly eristic. In this paper we explore this gap by bringing together the Argument Interchange Format (AIF) and the Semantic Interlinked Online Communities (SIOC) project, and modelling a sample of social web arguments. This allows us to explore which eristic effects cannot be modelled, and also to see which features of the social web are missing.We show that even in our small sample, from YouTube, Twitter and Facebook, eristic effects (such as playing to the audience) were missing from the final model, and that key social features (such as likes and dislikes) were also not represented. This suggests that both eristic and social extensions need to be made to our models of argumentation in order to deal effectively with the social we

The “Logic” of Informal Logic

Are there any logical norms for argument evaluation besides soundness and inductive strength? The paper will look at several concepts or models introduced over the years, including those of Wisdom, Toulmin, Wellman, Rescher, defeasible reasoning proponents and Walton to consider whether there is common ground among them that supplies an alternative to deductive validity and inductive strength

No Rationality Through Brute-Force

All reasoners described in the most widespread models of a rational reasoner exhibit logical omniscience, which is impossible for finite reasoners (real reasoners). The most common strategy for dealing with the problem of logical omniscience is to interpret the models using a notion of beliefs different from explicit beliefs. For example, the models could be interpreted as describing the beliefs that the reasoner would hold if the reasoner were able reason indefinitely (stable beliefs). Then the models would describe maximum rationality, which a finite reasoner can only approach in the limit of a reasoning sequence. This strategy has important consequences for epistemology. If a finite reasoner can only approach maximum rationality in the limit of a reasoning sequence, then the efficiency of reasoning is epistemically (and not only pragmatically) relevant. In this paper, I present an argument to this conclusion and discuss its consequences, as, for example, the vindication of the principle 'no rationality through brute-force'

Circularities In The Contemporary Philosophical Accounts Of The Applicability Of Mathematics In The Physical Universe

Contemporary philosophical accounts of the applicability of mathematics in physical sciences and the empirical world are based on formalized relations between the mathematical structures and the physical systems they are supposed to represent within the models. Such relations were constructed both to ensure an adequate representation and to allow a justification of the validity of the mathematical models as means of scientific inference. This article puts in evidence the various circularities (logical, epistemic, and of definition) that are present in these formal constructions and discusses them as an argument for the alternative semantic and propositional-structure accounts of the applicability of mathematics