M&M2014- Abstracts for Modality and Modalities, 2014
Staffan Angere
"Weakly definite descriptions"
In mathematics it is common to talk about objects defined up to isomorphism as if they were uniquely determined: we talk about “the” natural numbers even though they are determined only up to isomorphism, or for first-order arithmetic, only up to elementary equivalence. A common way to interpret this is to say that what we are "really" talking about is equivalence classes of models; however, this is not always possible to do consistently. The purpose of the talk is to show one way in which such practices can yet be made rigorous. For this we will employ a (presumably) new class of modal logics called transformational logics, and extend these with a version of the epsilon calculus. We show how to use such logics to define weakly definite description operators explicitly.
| weakdefdescr.pdf |
Martin Mose Bentzen
"Deontic reasoning and deontic logic"
What is the connection between the descriptive aspects and the normative aspects of logic? What should logicians do when people systematically reason in a way that is different from what is prescribed by standard logical systems? Can we accommodate linguistic intuitions without giving up on reason? In this talk, I propose an approach that might help us bridge the gap between the normative and the descriptive sides of logic, which I call reasoning systems. The basic idea is that inferences of a symbolic system will be perceived to be correct when there is alignment between an ideal model domain and a social domain. This correctness is ceteris paribus and we might consider changing either the model domain or the social domain in order to obtain perceived correctness of inferences. I apply this approach in an investigation of deontic reasoning. I review some work from the psychological literature about deontic reasoning. I present some results from an empirical study in deontic reasoning I have undertaken amongst Danish engineering students. I consider implications for deontic logic.
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Jens Christian Bjerring
"Impossible worlds, triviality, and duality."
To overcome the problem of logical omniscience, we may appeal to impossible worlds. By including in modal space impossible worlds where "anything goes'', logically speaking, it is easy to model agents who are incapable of performing even the most elementary logical deductions. But if we want to use the resulting framework to model minimally rational agents who are not logically omniscient but nevertheless logically competent, things look less bright. For it can be shown that it is impossible to construct a space of impossible worlds that can do this job and that satisfies certain standard conditions. Yet, for this result to have formal bite, the standard analysis of doxastic possibility must hold: a sentence A is doxastically possible for an agent just in case A is true at some world that is doxastically possible for the agent. But when doxastic necessity and possibility are duals, and when impossible worlds can be among the worlds that are doxastically possible for an agent, this analysis fails. In the talk, I argue that there are good reasons to give up the duality of doxastic necessity and possibility in an impossible worlds framework, and that a suitable interpretation of the modal notions can restore the full force of the impossibility result.
| impossible_worlds_triviality_and_duality.pdf |
Patrick Blackburn
"Now for Arthur Prior"
In this talk (which reports on ongoing work with Klaus Frovin Jørgensen) I will discuss Arthur Prior's paper 'Now'. This first appeared in 1968 in the journal Nous, and was written in response to Hans Kamp's pioneering two-dimensional analysis of the indexical adverb Now. It's a rich paper, with several asides, but the main point Prior makes is that is two-dimensional approach is unecessary. Moreover, in presenting his argument, Prior makes a brief (less than one page) but telling excursion into what is now known as hybrid logic. I will briefly sketch what Prior was attempting to do, and link his work with contemporary concerns.
- Thomas Bolander
"Bisimulation for multi-agent plausibility models"
"Bisimulation for multi-agent plausibility models"
Plausibility models are Kripke models agents use to reason about the knowledge and beliefs of themselves and each other -- and for revising their beliefs. When defining bisimulation for such plausibility models in the standard way in terms of the accessibility relations, one gets a notion of bisimulation that does not correspond to modal equivalence. In the talk, I will define an alternative notion of bisimulation that gives the expected correspondence to modal equivalence. I will then investigate bisimulations for the logic of conditional beliefs, the logic of degrees of belief and the logic of safe belief, and compare expressive power of these languages. Surprisingly, the logic of conditional beliefs and the logic of degrees of belief turn out to be expressively incomparable.
This is joint work with Mikkel Birkegaard Andersen, Hans van Ditmarsch and Martin Holm Jensen.
This is joint work with Mikkel Birkegaard Andersen, Hans van Ditmarsch and Martin Holm Jensen.
| bisimulation.pdf |
- Torben Braüner
- "Hybrid-Logical Proofs: With an Application to the Sally-Anne Task"
This additional expressive power of hybrid logic is useful for many applications. I start my talk by giving a brief introduction to proof systems for hybrid logic. I then show how a hybrid-logical proof system can be used to formalize the so-called Sally-Anne task which is used in cognitive psychology to test theory of mind. Giving a correct answer to the Sally-Anne task requires a shift from one's own perspective to another perspective. This perspective shift can be handled directly in hybrid logic by letting points in a model represent perspectives. I compare to two other formalizations of the Sally-Anne task; one given by Stenning and van Lambalgen, and one given by Arkoudas and Bringsjord.
| mm2014.pdf |
- Zoé Christoff
- "A minimal dynamic logic for threshold influence"
We take a logical approach to so-called threshold models, used to study the diffusion of a new technology, fashion, opinion, behaviour , etc. within social networks. Threshold models consist of a network graph of agents connected by a social relationship and a fixed threshold to adopt a given new behaviour. The diffusion relies on the following assumption: an agent adopts the new behaviour when the proportion of his network-neighbours who have already adopted it reaches the given threshold. I will present a minimal dynamic logic to reason about such threshold dynamics. Rasmus K. Rendsvig will then discuss in his talk how to extend this framework with an epistemic dimension to model how information about the behaviour of others interacts with the diffusion dynamics .
| mm2014_-_dynamic_logic_for_threshold_models.pdf |
- Giovanni Cina and Sebastian Enqvist
- "Modal correspondence theory over presheaves"
In this talk we will outline some work in progress in the area at the interface of Modal Logic and Category Theory. We will focus on presheaf categories and on a construction called the category of elements.
If the objects of the base category are regarded as path objects (that is, computational-path shapes) then we follow the steps of Winskel, Nielsen and others, who investigated the characterization of the notion of bisimulation in terms of spans of open maps and so called "path bisimulations". These authors also introduced a modal logic for presheaf models, called "path logic". In our talk, we show that we can also associate a multisorted first-order logic with any path category in a natural way.
We present a few first observations about the relationship between this first-order language and path logic. First, we note that an analogue of van Benthem's well known characterization of modal logic as the "bisimulation invariant fragment of FOL" holds for the path logic relative to any given base category. Interestingly, this gives a correspondence result in some cases where the van Benthem's theorem fails for standard FOL: an example is the base category called L*, presheaves over which correspond to labelled synchronization trees. Restricted to the class of synchronization trees, the bisimulation invariant fragment of (standard, one-sorted) FOL is strictly more expressive than basic modal logic. As a second observation, we note that in the case of the base category L*, it is decidable whether a formula of the multi-sorted first-order language is equivalent to a formula of path logic. Again, this is in contrast with the situation in classical correspondence theory, where the question of whether a given FOL-formula is equivalent to a modal formula is known to be undecidable. As a final observation, we note that the multi-sorted first-order logic for L* is itself decidable.
If the objects of the base category are regarded as path objects (that is, computational-path shapes) then we follow the steps of Winskel, Nielsen and others, who investigated the characterization of the notion of bisimulation in terms of spans of open maps and so called "path bisimulations". These authors also introduced a modal logic for presheaf models, called "path logic". In our talk, we show that we can also associate a multisorted first-order logic with any path category in a natural way.
We present a few first observations about the relationship between this first-order language and path logic. First, we note that an analogue of van Benthem's well known characterization of modal logic as the "bisimulation invariant fragment of FOL" holds for the path logic relative to any given base category. Interestingly, this gives a correspondence result in some cases where the van Benthem's theorem fails for standard FOL: an example is the base category called L*, presheaves over which correspond to labelled synchronization trees. Restricted to the class of synchronization trees, the bisimulation invariant fragment of (standard, one-sorted) FOL is strictly more expressive than basic modal logic. As a second observation, we note that in the case of the base category L*, it is decidable whether a formula of the multi-sorted first-order language is equivalent to a formula of path logic. Again, this is in contrast with the situation in classical correspondence theory, where the question of whether a given FOL-formula is equivalent to a modal formula is known to be undecidable. As a final observation, we note that the multi-sorted first-order logic for L* is itself decidable.
| presentation_lund.pdf |
- Melvin Fitting
- "The Range of Realization"
Justification logics are explicit versions of modal logics. Modal operators are replaced with justification terms, representing moves in a proof construction. Justification logics are connected with modal logics via Realization Theorems. These say that modal operators in a theorem can be replaces with justification terms to produce an explicit version of the theorem. The first Realization Theorem connected modal S4 with justification LP (logic of proofs). But now it is becoming clear that the phenomenon is a much more general one than had been supposed.
I will discuss the historical origin of Justification Logics, and their corresponding Realization Theorems. Then I will bring things up to date, with the current state of affairs. The range of modal logics to which this applies is larger than had been expected. Along the way the role of constructive vs nonconstructive arguments will be considered. And computer implementations will be briefly touched on.
I will discuss the historical origin of Justification Logics, and their corresponding Realization Theorems. Then I will bring things up to date, with the current state of affairs. The range of modal logics to which this applies is larger than had been expected. Along the way the role of constructive vs nonconstructive arguments will be considered. And computer implementations will be briefly touched on.
| 2014_lund_realization.pdf |
- Valentin Goranko
- "On knowledge and ignorance"
Traditionally, knowledge is modelled in epistemic logic as lack of uncertainty. On the other hand, lack of knowledge is often called ignorance. But, ignorance and uncertainty are different concepts. So, how should we model ignorance and formalise reasoning about ignorance? How ignorant can an agent be? How mutually ignorant can two agents be? I will discuss these and related questions and some challenges in capturing and formalizing adequately the relationship between knowledge and ignorance.
- Jens Ulrik Hansen
- "A fuzzy hybrid logic and opinion dynamics in social networks"
In this talk, I will introduce a many-valued logic that borrows elements from Modal Logic, Hybrid Logic, and Fuzzy Logic to reason about a model of opinion dynamics in social networks initially proposed by Morris DeGroot (1974). Along the road, I will first explain why modal and hybrid logic, in an egocentric reading, are particularly well suited for reasoning about social networks and their dynamics. Then, I will explain DeGroot’s model of opinion dynamics in social networks and why a many-valued Fuzzy Logic is needed. Finally, I will put it all together in a logic for reasoning about opinion dynamics in social networks and exemplify its usefulness.
| a_fuzzy_hybrid_logic_and_opinion_dynamics_in_social_networks.pdf |
- Martin Holm Jensen
"Unsupervised Language Acquisition by Children with Special Needs"
"Unsupervised Language Acquisition by Children with Special Needs"
Children with special needs are often impaired when it comes to acquiring language. Overcoming this requires tedious repetition of language related tasks at a very early age. In order to develop a cognitive connection between language and the real world, these tasks should combine both non-physical and physical elements. Digiplay is a product currently under development that facilitates such language tasks. Unsupervised use of this product requires a method for selecting the task that a given child should be presented with, so that she is properly challenged and wants to do more repetitions. This would free up resources in child care centres and additionally allow for the product to be used at home. In this talk I will present the Digiplay product in its current form, and discuss our approach to developing an unsupervised version of it.
| slides.pdf |
- Klaus Frovin Jørgensen
"On the Development of a Seligman-Stye Tableau System for Hybrid Logic"
- Klaus Frovin Jørgensen
"On the Development of a Seligman-Stye Tableau System for Hybrid Logic"
This talk is about the development of a new tableau system for hybrid logic. Patrick Blackburn, Thomas Bolander, Torben Bräuner and I have developed a tableau calculus where rules are given for *all* types of formulas of a the basic hybrid language. This is in contrast with existing tableau systems, where formulas have to be satisfaction statements or negations of such. In doing this we follow work done by Jerry Seligman dating back to the late 90s. The tableau calculus for the basic propositional hybrid system is complete, and a restricted version of the calculus is terminating, but still compete. Further work on the extensions (downarrow, universal modality, first order) of our work is briefly discussed.
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- Sara Negri
"Proof systems for normal modal logics with arbitrary
first-order frame conditions"
- Sara Negri
"Proof systems for normal modal logics with arbitrary
first-order frame conditions"
A uniform method was presented in Negri (2005) for obtaining complete proof systems for all modal logics characterised by what are known as geometric frame conditions.
Motivated by a proof-theoretical investigation of the Church-Fitch knowability paradox (Maffezioli, Naibo and Negri 2013), wider classes of modal logics were
studied and shown amenable to a similar treatment through a generalisation of the method of axioms as rules (Negri 2014).
In this talk, it is shown how to turn arbitrary first-order frame conditions into a finite collection of local geometric rules, through an appropriate conservative semidefinitional extension of the language. In particular, this ``geometrization of first order logic'' yields complete sequent calculi for all modal logics defined by first-order frame conditions (Dyckhoff and Negri 2014).
References:
Dyckhoff, R. and S. Negri (2014) Geometrization of first-order logic, ms.
Maffezioli, P., A. Naibo, and S. Negri (2013) The Church-Fitch
knowability paradox in the light of structural proof theory. Synthese,
vol. 190, pp. 2677-2716.
Negri, S. (2005) Proof analysis in modal logic. Journal of
Philosophical Logic, vol. 34, pp. 507-544.
Negri, S. (2014) Proof analysis beyond geometric theories: from rule
systems to systems of rules.
Journal of Logic and Computation, in press.
Motivated by a proof-theoretical investigation of the Church-Fitch knowability paradox (Maffezioli, Naibo and Negri 2013), wider classes of modal logics were
studied and shown amenable to a similar treatment through a generalisation of the method of axioms as rules (Negri 2014).
In this talk, it is shown how to turn arbitrary first-order frame conditions into a finite collection of local geometric rules, through an appropriate conservative semidefinitional extension of the language. In particular, this ``geometrization of first order logic'' yields complete sequent calculi for all modal logics defined by first-order frame conditions (Dyckhoff and Negri 2014).
References:
Dyckhoff, R. and S. Negri (2014) Geometrization of first-order logic, ms.
Maffezioli, P., A. Naibo, and S. Negri (2013) The Church-Fitch
knowability paradox in the light of structural proof theory. Synthese,
vol. 190, pp. 2677-2716.
Negri, S. (2005) Proof analysis in modal logic. Journal of
Philosophical Logic, vol. 34, pp. 507-544.
Negri, S. (2014) Proof analysis beyond geometric theories: from rule
systems to systems of rules.
Journal of Logic and Computation, in press.
Nikolaj Nottelmann
"A new kind of unsafe knowledge"
Several prominent epistemologists have proposed that safety is at least a necessary requirement for knowledge. However, over the last years a literature of counter-examples to this claim has emerged. In this talk I review typical alleged counter-examples found in the literature and propose a hopefully convincing case of unsafe knowledge in a novel mould. Finally, I discuss the epistemological implications of regarding safety as a condition, which is typically satisfied when a subject knows, but need not be.
| presentation_-_mm_may23-14.pptx |
Peter Øhrstrøm
"Prior's Logical Analysis of the Ontological Argument"
A.N. Prior (1914-69) found Anselm's so-called ontological argument for the existence of God rather interesting. In his publications he contributed significantly to the logical and conceptual analysis of Anselm’s argument, and it is evident from his unpublished papers and his letters that he was struggling in order to obtain a deeper understanding of the logical and philosophical problems related to the argument. In particular, Prior focussed on the notions of existence and on the use modal logic in the various versions of the argument.
In this paper I intend to discuss some important aspects of Prior's work on the topics related to the ontological argument as we know this work from his publications and from his unpublished papers and letters.
In this paper I intend to discuss some important aspects of Prior's work on the topics related to the ontological argument as we know this work from his publications and from his unpublished papers and letters.
| priorontologicalargument2.pdf |
- Carlo Proietti
"The knowability paradox. An approach with quantified modal logic"
"The knowability paradox. An approach with quantified modal logic"
The knowability paradox (Fitch, 1963) consists of a derivation of (a) p -> Kp from (b) p -> MKp.
An intuitive reading of this argument is that “All truths are knowable” (weak verificationism) entails that “All truths are known” (strong verificationism). As a consequence, verificationists and anti-realists are in trouble because one of their basic claims entails a blatant absurdity. Therefore, verificationism and anti-realism are problematic on a simple logical basis.
Among other purported solutions of the paradox, so-called reformulation strategies - inaugurated by D. Edgington (1985) - deny that p -> MKp is an adequate formal rendering of weak verificationism. Supporters of these solutions claim that the problem is due to a limited expressivity of modal propositional languages. The essential core of these proposals is that "All truth are knowable" should be read as "All actual truths are possibly known by some (actual or non-actual) knower to be true of the actual situation". Despite their intuitive plausibility these solutions face many technical problems.
I claim, in the spirit of Kvanvig (2006), that for a better understanding of the problem we need to reformulate verificationist theses in a first-order modal language which allows de re/ de dicto specifications and indexing individuals, quantifiers and properties to specific possible worlds. In one word, a first-order hybrid modal logic.
Here I will formulate my proposal for which it turns out, among other things, that:
1) There are many possible renderings of weak verificationism
2) The weak verification thesis is not expressible by a fix substitution-free schema, but rather via a translational schema
3) In the new framework the corresponding paradox is avoided without (hopefully) falling into the technical and philosophical problems affecting previous solutions of this kind.
An intuitive reading of this argument is that “All truths are knowable” (weak verificationism) entails that “All truths are known” (strong verificationism). As a consequence, verificationists and anti-realists are in trouble because one of their basic claims entails a blatant absurdity. Therefore, verificationism and anti-realism are problematic on a simple logical basis.
Among other purported solutions of the paradox, so-called reformulation strategies - inaugurated by D. Edgington (1985) - deny that p -> MKp is an adequate formal rendering of weak verificationism. Supporters of these solutions claim that the problem is due to a limited expressivity of modal propositional languages. The essential core of these proposals is that "All truth are knowable" should be read as "All actual truths are possibly known by some (actual or non-actual) knower to be true of the actual situation". Despite their intuitive plausibility these solutions face many technical problems.
I claim, in the spirit of Kvanvig (2006), that for a better understanding of the problem we need to reformulate verificationist theses in a first-order modal language which allows de re/ de dicto specifications and indexing individuals, quantifiers and properties to specific possible worlds. In one word, a first-order hybrid modal logic.
Here I will formulate my proposal for which it turns out, among other things, that:
1) There are many possible renderings of weak verificationism
2) The weak verification thesis is not expressible by a fix substitution-free schema, but rather via a translational schema
3) In the new framework the corresponding paradox is avoided without (hopefully) falling into the technical and philosophical problems affecting previous solutions of this kind.
| fitch_and_foml_052014.pdf |
- Rasmus K. Rendsvig
"An Epistemic Extension of Threshold Models: Coordinating based on Behavior Prediction"
"An Epistemic Extension of Threshold Models: Coordinating based on Behavior Prediction"
We extend the framework of threshold models (see abstract of Zoé Christoff) with an epistemic dimension and investigate how information about more distant neighbors’ behaviors allows agents to anticipate changes in behavior of their closer neighbors. It is shown that this epistemic prediction dynamics is equivalent to the non-epistemic threshold model dynamics if and only if agents know exactly their neighbors’ behavior. We further show results regarding fixed points and convergence speed of the prediction dynamics.
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- Jerry Seligman
"Understanding some pathologies of social epistemology by reasoning about observed behaviour"
"Understanding some pathologies of social epistemology by reasoning about observed behaviour"
Whereas spoken announcements are common fare for epistemic logicians, gestures and other vision-based signals are less well-studied. We propose a logic for reasoning about observed behaviour and apply it to the analysis of certain well-known pathologies of social psychology: pluralistic ignorance and the bystander effect. (This talk will report on recent joint work with Liang Zhen.)
| seeing-lund.pdf |
- Sonja Smets
"The Epistemic Potential of Groups"
"The Epistemic Potential of Groups"
In this presentation I focus on the ‘epistemic potential' of a group of agents, i.e. the knowledge (or beliefs) that the group may come to possess if all its members join their forces and share their individual information. Among the different notions of group knowledge studied in the literature, which one can give us a good measure of a group's epistemic potential? A first candidate is `distributed knowledge', which can in principle be converted into actual individual knowledge by means of simple inter-agent communication. However in practice there are many factors which may prevent the full actualization of distributed knowledge. These factors include the group's dynamics, the structure of the social network, the individuals' different epistemic interests and agendas, etc. When we take these realistic conditions into account, a more accurate formalization of a group's potential knowledge can be developed. I show that in scenarios allowing inter-agent communication as the group's main knowledge-aggregation method, the group's true epistemic potential may well turn out to be very different from both distributed knowledge and from common knowledge (lying instead somewhere in between these extremes). The results reported on in this lecture are based on on-going joint work with A. Baltag and R. Boddy at the University of Amsterdam.
- Sara Uckelman
"Medieval Modal Logic: What Is It, Where Can You Find It, And What Can You Do With It Once You've Got It"
"Medieval Modal Logic: What Is It, Where Can You Find It, And What Can You Do With It Once You've Got It"
The High Middle Ages in Europe, from roughly the end of the 11th C to the end of the 14th C, was a period of rapid and diverse innovation in logic. And yet, because for so long material from this period was available only in Latin, very few contemporary logicians know much about medieval developments. In this tutorial, I'll address the three
questions posed in the title, presupposing no knowledge of medieval logic. While the focus will be on modalities and their occurrences in medieval philosophical and logical discussions, there will also be digressions into other topics in medieval logic as necessary to make the discussion clear. At the end, people will hopefully go away with an idea of the extremely broad range of interesting research topics available in this field, as well as a handle on how to go about accessing the necessary sources to do first-hand research on the topic.
questions posed in the title, presupposing no knowledge of medieval logic. While the focus will be on modalities and their occurrences in medieval philosophical and logical discussions, there will also be digressions into other topics in medieval logic as necessary to make the discussion clear. At the end, people will hopefully go away with an idea of the extremely broad range of interesting research topics available in this field, as well as a handle on how to go about accessing the necessary sources to do first-hand research on the topic.
| m-and-m.pdf |
- Timothy Williamson
"Abductive Method in Modal Logic"
"Abductive Method in Modal Logic"
In this informal methodological talk, I will explain the role of an abductive methodology similar to that of natural science in the development of interpreted modal logics, with special reference to comprehension principles in higher-order modal logic and the application of mathematics to counterfactual situations.
