Spring Semester FS2022

Unless stated otherwise, all talks will take place in room A97 of the Exakte Wissenschaft Building (ExWi) at the University of Bern.

Schedule

Abstracts

In this talk, I develop and defend Reason Structuralism. Reason Structuralism holds that reasons are individuated by their place in a structure, rather than by their intrinsic properties. The place of a reason in a structure is individuated along two dimensions: first, at the level of content, and second, at the level of support. I compare Reason Structuralism to some alternatives and to mathematical structuralism. I give identity criteria for reasons based on automorphisms and sketch some ideas for a logic of reason terms. Finally, I give an abductive argument for the view: reason structuralism has theoretical advantages and greater explanatory power over other options.

A distributive l-monoid is a lattice-ordered monoid with a distributive lattice reduct such that the product distributes over both binary meets and binary joins. The class of distributive l-monoids forms a variety (equational class). A distributive l-monoid is called idempotent or commutative if its monoid reduct is idempotent or commutative, respectively, and it is called semilinear if it is contained in the variety generated by the class of totally ordered monoids. In this talk I will present some structural results about the variety SemIdDLM of semilinear idempotent distributive l-monoids and its commutative subvariety CIdDLM. In particular, I will present a decomposition result for finite totally ordered idempotent monoids and an explicit characterization of the finite subdirectly irreducible members of SemIdDLM in terms of this decomposition. A consequence of this characterization is that the subvariety lattice of SemIdDLM is countably infinite. In the commutative case the decomposition even leads to an explicit description of the subvariety lattice of CIdDLM.

Traditionally, emotions were seen as irrational behavior that disrupts rationality. It has been replaced by the pro-emotion consensus that claims that emotion is complementary to rational thinking and behavior, and in support of these. We use these insights for artificial intelligence because it can help not only to get artefacts with a more human-like behavior thus having deeper and more meaningful human-machine relationship, but also to direct agents' attention to what is relevant, important and significant in order to ensure effective behavior. This talk will present the logical models of various types of emotions as well as two mechanisms underlying the social effects of emotions.

I will present investigations of a non-classical version of linear temporal logic (with next, eventually, and henceforth modalities) whose propositional fragment is Gödel–Dummett logic (which is well known both as a superintuitionistic logic and a t-norm fuzzy logic). We define the logic using two natural semantics—a real-valued semantics and a semantics where truth values are captured by a linear Kripke frame—and can show that these indeed define one and the same logic. Although this Gödel temporal logic does not have any form of the finite model property for these two semantics, we are able to prove decidability of the validity problem. The proof makes use of quasimodels, which are a variation on Kripke models where time can be nondeterministic. We can show that every falsifiable formula is falsifiable on a finite quasimodel, which yields decidability. We then strengthen this result to PSPACE-complete. Further, we provide a deductive calculus for Gödel temporal logic with a finite number of axioms and deduction rules, and can show this calculus to be sound and complete for the above-mentioned semantics. This is joint work with Juan Pablo Aguilera, Martín Diéguez, and David Fernandez-Duque.

Paradoxes of material implication were some of the main motivations in the early development of modern modal logic. Many such paradoxes can be avoided by considering an alternative implication connective, called strict implication, that arises from prefixing material implication by a modal necessity operator. From the perspective of Kripke semantics, strict implication addresses the defects of material implication essentially by filtering them out in the passage from individual worlds to global characteristics of Kripke models. Nevertheless, many important features of the local, classical logic of worlds in Kripke models survive in transitioning to the global structure. In this talk, I report on my recent work toward understanding logical local-to-global principles through the lens of non-classical variants of strict implication.

Gossip describes the spread of information throughout a network of agents. In Dynamic Gossip the network can grow at run-time. Most gossip protocols assume that all agents are reliable, but this is not given for many practical applications. We drop this assumption and study Dynamic Gossip with unreliable agents that "lie" about their own secret. We show that protocols from the literature no longer work with unreliable agents, in the sense that they no longer characterize the same networks. In addition, we show that unreliable agents that do not initiate communication are harder to identify than agents that do. This has paradoxical consequences for measures against unreliability, for example to combat the spread of false information in social networks. This is joint work with Malvin Gattinger (ILLC, University of Amsterdam)

Prime factorization was thought to be hard (i.e. not solvable in polynomial time) and is therefore the basis for the widespread cryptosystem RSA. In 1994 Peter W. Shor proposed an algorithm , for a quantum computer, that can solve the problem efficiently(i.e. in polynomial steps) . In this talk i will present this algorithm, and the necessary, theoretical, quantum circuits to implement it.

A proposition p is common knowledge among a group of agents if all agents know p, all agents know, that all agents know p, and so on. In a formal setting, common knowledge is studied using the so-called common knowledge logic CKL, which is an extension of multi-modal logic with a fixed point operator. CKL is most often interpreted over S5 Kripke frames. Nevertheless, the proof theory for CKL over S5 is quite underdeveloped. In particular, it is an open question whether there exists an analytic sequent calculus for CKL over S5, i.e. a calculus in which every valid sequent admits a proof consisting only of formulas relevant to the endsequent. In this talk I present a positive answer to that question. I will introduce a cyclic sequent calculus for CKL over S5, which is analytically complete. I will sketch soundness and completeness proofs, demonstrate that the calculus is suitable for proof search and compare it to other approaches to obtain an analytic system. This is joint work with Jan Rooduijn (ILLC, University of Amsterdam).

We call terms t_1,...,t_n V-dependent if there is a non-valid equation in y_1,...,y_n such that the equation, where the y_i are substituted by the t_i, is valid in V. The dependence-problem is then the problem of deciding whether any finite number of terms are V-dependent. In this talk I give a small introduction to dependence and show that the dependence-problem for the varieties of modal join-semilattices and modal meet-semilattices is decidable.

Two-layered modal syntax is given by three propositional languages: the inner one (also known as the language of events), the modal one (whose connectives are actually called modalities), and the outer one (also known as the language of statements). Early examples of logics with two-layered syntax were modal logics of probability developed by Hamblin, Fagin, Halpern governed by classical logic on both layers. Later Hajek with his coauthors considered alternative non-classical logics for both the outer layer (to speak directly about probabilities of events) and inner layer (to speak about uncertainty of vague events). Subsequently, numerous other examples of such logics were described and developed in the literature thus constituting an area of logic screaming for systematization through the development and application of uniform, general, and abstract methods. The first steps towards such theory were taken in my WoLLIC paper coauthored by Carles Noguera; the aim of this talk is to present the state of the art of its development.