Logic, Rationality, and Interaction

We introduce Coalition Logic for Resource Games (CLRG) which extends Coalition Logic by allowing explicit reasoning about resource endowments of coalitions of agents and resource bounds on strategies. We show how to express interesting properties of coalitional ability under resource bounds in this logic, including properties of Coalitional Resource Games introduced by Wooldridge and Dunne in [1]. We also give an efficient model-checking algorithm for CLRG which makes it possible to verify the properties automatically.

Building on a simple modal logic of context, the paper presents a dynamic logic characterizing operations of contraction and expansion on theories. We investigate the mathematical properties of the logic, and show how it can capture some aspects of the dynamics of normative systems once they are viewed as logical theories.

Questions are triggers for explicit events of ‘issue management’. We give a complete logic in dynamic-epistemic style for events of raising, refining, and resolving an issue, all in the presence of information flow through observation or communication. We explore extensions of the framework to longer-term temporal protocols and multi-agent scenarios. We sketch a comparison with two main alternative accounts: Hintikka’s interrogative logic and Groenendijk’s inquisitive semantics.

Most belief change operators in the AGM tradition assume an underlying plausibility ordering over the possible worlds which is transitive and

complete

. A unifying structure for these operators, based on supplementing the plausibility ordering with a second, guiding, relation over the worlds was presented in [5]. However it is not always reasonable to assume completeness of the underlying ordering. In this paper we generalise the structure of [5] to allow incomparabilities between worlds. We axiomatise the resulting class of belief removal functions, and show that it includes an important family of removal functions based on

finite prioritised belief bases

.

Inquisitive semantics (cf. Groenendijk, 2008) provides a formal framework for reasoning about information exchange. The central logical notion that the semantics gives rise to is

compliance

. This paper presents an algorithm that computes the set of compliant responses to a given initiative. The algorithm is sound and complete. The implementation is accessible online via

www.illc.uva.nl/inquisitive-semantics

.

One important function of logics of agency (Stit Logic, ATL, CL, Dynamic Logic) is to assess the validity of arguments whereby responsibility is attributed to, or denied by, individuals and groups. Indeed, the vocabulary and computational properties of such logic allow us to express and reason on what agents did, or what empowered them to do (either following a strategy as in ATL or not). It is clear that this kind of reasoning is indispensable when we want to attribute or distribute responsibility to agents, as when we want to ascertain that some agents were not responsible of the events into account: if the group constituted by two persons

did not

or even

could not

for some reasons blow a hospital, then they should not be charged for blowing the hospital. Agency and the formal framework for it then appear to be important for the implementation of a rigourous reasoning on responsibility in (or of) groups.

Iterated dominance is perhaps the most basic principle in game theory. The epistemic foundation of this principle is based on the assumption that all players are rational. The main contribution of this paper is to characterize the algorithm of iterated admissibility in Probabilistic Epistemic Game Logic (PEGL). Firstly, on the basis of Probabilistic Epistemic Logic we set up a logic PEGL. Secondly, by redefining a concept of rationality, we show that the common knowledge of the rationality characterizes the algorithm of Iterated Admissibility, that is, we provide an epistemic foundation for the solutions or equilibria which are found by the algorithm of Iterated Admissibility(IA). Next, we provide a different characterization of IA using public announcements of the rationality in dynamic logic. The results we obtain can be seen as giving a dynamic epistemic foundation for the algorithm of Iterated Admissibility.

Formal learning theory formalizes the phenomenon of language acquisition. The theory focuses on various properties of the process of

conjecture-change over time

, and therefore it is also applicable in philosophy of science, where it can be interpreted as a theory of empirical inquiry. Treating “conjectures” as beliefs, we link the process of conjecture-change to doxastic update. Using this approach, we reconstruct and analyze the temporal aspect of learning in the context of temporal and dynamic logics of belief change. We provide a translation of learning scenarios into the domain of dynamic doxastic epistemic logic. Then, we express the problem of finite identifiability as a problem of epistemic temporal logic model checking. Furthermore, we prove a doxastic epistemic temporal logic representation result corresponding to an important theorem from learning theory, that characterizes identifiability in the limit, namely Angluin’s theorem. In the end we discuss consequences and possible extensions of our work.

In this paper we study Aumann’s Agreement Theorem in dynamic-epistemic logic. We show that common

belief

of posteriors is sufficient for agreements in “epistemic-plausibility models”, under common and well-founded priors, from which the usual form of agreement results follows, using common knowledge. We do not restrict ourselves to the finite case, and show that in countable structures such results hold if

and only if

the underlying “plausibility ordering” is well-founded. We look at these results from a syntactic point of view, showing that neither well-foundedness nor common priors are expressible in a commonly used language, but that the static agreement result is finitely derivable in an extended modal logic. We finally consider “dynamic” agreement results, show they have a counterpart in epistemic-plausibility models, and provide a new form of agreements via “public announcements”. Comparison of the two types of dynamic agreement reveals that they can indeed be different.

In formal approaches to inductive learning, the ability to learn is understood as the ability to single out a correct hypothesis from a range of possibilities. Although most of the existing research focuses on the characteristics of the learner, in many paradigms the significance of the teacher’s abilities and strategies is in fact undeniable. Motivated by this observation, this paper highlights the interactive nature of learning by showing its relation with games. We show how learning can be seen as a

sabotage-type

game between

Teacher

and

Learner

, and we present different variants based on the level of cooperativeness and the actions available to the players, characterizing the existence of winning strategies by formulas of

Sabotage Modal Logic

and analyzing their complexity. We also give a two-way conceptual account of how to further combine games and learning: we propose to use game theory to analyze the grammar inference approach, and moreover, we indicate that existing inductive inference games can be analyzed using learning theory tools. Our work aims at unifying game-theoretical and logical approach to formal learning theory.

Arrow’s Theorem is a central result in social choice theory. It states that, under certain natural conditions, it is impossible to aggregate the preferences of a finite set of individuals into a social preference ordering. We formalise this result in the language of first-order logic, thereby reducing Arrow’s Theorem to a statement saying that a given set of first-order formulas does not possess a finite model. In the long run, we hope that this formalisation can serve as the basis for a fully automated proof of Arrow’s Theorem and similar results in social choice theory. We prove that this is possible in principle, at least for a fixed number of individuals, and we report on initial experiments with automated reasoning tools.

By moving from a suggestive example, the paper analyzes how information flows among agents involved in a deliberation. By deliberating, agents become aware of details, draw the attention of the group to some issues, perform inferences and announce what they know. The proposed framework—which builds on the paradigm of dynamic logic—captures how, during a deliberation, information results from step-wise multi-agent interaction.

We introduce a

dynamic testimonial logic

(DTL) to model belief change over sequences of multi-agent testimony. Our static base logic is Baltag and Smets’ [1]

conditional doxastic logic

(CDL). Our dynamic base logic is van Benthem’s [12]

dynamic logic of belief upgrade

, which we extend with a “belief suspension” operator. After showing how to extract from CDL models agents’ beliefs about the

doxastic reliability

of other agents, we add “authority graphs” to DTL models to capture agents’

epistemic trust

in other agents’ testimony. For DTL’s dynamic testimony operator, we give complete reduction axioms. Finally, we describe an application of DTL in modeling

epistemic bandwagon effects

.

The standard approach to a rational action paradox in game theory (namely, the chain store paradox) has presupposed that the player’s beliefs are probabilities represented by functions with values between 0 and 1. However, a general solution must include the possibility that the subjective probabilities take only the values 1 and 0, requiring a non-Bayesian account of belief revision. In this paper, we propose a situation-theoretic diagnosis and solution to the paradox, based on the conception of Austinian propositions relativized to particular situations, as developed by Barwise and Etchemendy.

Two types of game structures for logics of ability have been proposed: Concurrent game structures and models of propositional control. The former takes an abstract view and can be used for general purposes; the latter is a restriction but is much easier for implementation. We present a game structure in between namely a declaration structure. A cooperation logic based on declaration structures is given. We present its deductive system and algorithms for model checking and satisfiability checking.

The aim of this work is propose a logical approach to intention dynamics based on the notion of

assignment

[3, 7]. The function of an assignment is to associate the truth value of a certain formula

ϕ

to a propositional atom

p

. We combine a static modal logic of belief and choice with three kinds of dynamic modalities and corresponding three kinds of assignments: assignments operating on an agent’s beliefs, assignments operating on the agent’s choices and assignments operating on the objective world. An agent’s intention is defined in our approach as the agent’s choice to perform a given action and two basic operations on intentions called intention generation and intention reconsideration are defined as specific kinds of assignments on choices.

We propose a modal logic called

$\mathcal{EDLA}$

(

Epistemic Dynamic Logic of Agency

) that allows to reason about epistemic games in strategic form.

$\mathcal{EDLA}$

integrates the concepts of joint action, preference and knowledge. In the first part of the paper we introduce

$\mathcal{EDLA}$

and provide soundness, completeness and complexity results. In the second part we study in

$\mathcal{EDLA}$

the epistemic and rationality conditions of some classical solution concepts like Nash equilibrium and iterated strict dominance. In the last part of the paper we combine

$\mathcal{EDLA}$

with Dynamic Epistemic Logic (DEL) in order to model epistemic game dynamics.

Following the approach given by Nina Gierasimczuk [2009] to bridge dynamic epistemic logic and learning theory, the logic of finite identification in the limit in the process of learning has been explored in this paper. The main results are two complete axiomatic systems. One is defined in terms of public announcements, and the other in terms of update by event models.

We suggest that in the context of planning in uncertain environments, an agent’s performance of an action may be tentative and not definitive. In this view, an agent plans to merely

try

performing an action, and further planning is dependent on the success or failure of such a trial. Epistemic logics seem well suited to formalize the reasoning in such contexts. We study a simple such logic for one planning agent making bounded plans, for which we give a complete axiomatization and prove decidability. We discuss preliminary results for extensions to multi-agent plans as well as unbounded plans.

In this paper, we suggest defining obligations under the assumption that agents are responsible. We consider how the framework developed by Horty in [2] can be modified to incorporate this idea, and how this solves some objections raised to Horty’s system. Also, we discuss how the assumption of a responsible world can (not easily) be incorporated into the framework of knowledge based obligations introduced by Pacuit, Parikh and Cogan in [5].

We introduce a new type of arrow in the

update frames

(or “action models”) of

Dynamic Epistemic Logic

in a way that enables us to reason about epistemic temporal dynamics in multi-agent systems that

need not be synchronous

. Since van Benthem and Pacuit (later joined by Hoshi and Gerbrandy) showed that standard Dynamic Epistemic Logic necessarily satisfies

synchronicity

, it follows that our arrow type is a new way of extending the domain of applicability of the Dynamic Epistemic Logic approach. Furthermore, our framework provides a new perspective on the van Benthem et al work itself. In particular, while each of our work and their work shows that epistemic temporal models generated by standard update frames necessarily satisfy certain structural properties such as synchronicity, our work clarifies the way in which these structural properties arise as a result of the inherent structure of standard update frames themselves.

The contemporary development of deontic logic since von Wright has been based on the study of the analogies between normative and alethic modalities. The weakest deontic logic called standard deontic logic (

SDL

) is the modal system of type

KD

. Jones and Sergot argued that contrary-to-duty (CTD) reasoning was necessary to represent the legal codes in legal expert systems. This reasoning invites such CTD paradoxes as Chisholm’s Paradox of SDL that is monadic. Hansson’s dyadic deontic logic can avoid CTD paradoxes. But it introduces such dilemmas as the Considerate Assassin’s Dilemma. Prakken and Sergot, and van der Torre and Tan proposed preference-based dyadic deontic logics that can explain away this dilemma. However, these logics face the Fundamental Problem of Intrinsic Preference. The aim of this paper is to propose a new non-modal logical version of complete and decidable preference-based dyadic deontic logic–conditional expected utility maximiser’s deontic logic (

CEUMDL

) that can avoid Chisholm’s Paradox and explain away the Considerate Assassin’s Dilemma. In the model of

CEUMDL

we can explain an agent’s preferences in terms of his degrees of belief and degrees of desire via conditional expected utility maximisation, which can avoid the Fundamental Problem of Intrinsic Preference and furnish a solution to the Gambling Problem. We provide

CEUMDL

with a Domotor-type model that is a kind of measurement-theoretic and decision-theoretic one.

Coalition Logic does not explicitly talk about the effects of a coalitional move on the strategic ability of the remaining players, while in Game Theory reasoning patterns involving this concept often occur. To fill this gap, we study an update operator for strategic ability update in coalition structures. Its formal connections with the update operators known from Dynamic Epistemic Logic will be discussed.

We study games in the presence of an interaction structure, which allows players to communicate their preferences, assuming that each player initially only knows his own preferences. We study the outcomes of iterated elimination of strictly dominated strategies (IESDS) that can be obtained in any given state of communication.

We also give epistemic foundations for these “intermediate” IESDS outcomes. This involves firstly describing the knowledge that the players would have in any state of communication, using the framework from Apt et al. [3]. We then prove that when there is common knowledge of rationality, each intermediate outcome is entailed by the knowledge in the relevant state of communication.

Social dilemma is a situation in which individual rationality leads to collective irrationality. That is, individually reasonable behavior leads to a situation in which everyone is worse off than they might have been otherwise [Kol98]. There are four types of social dilemmas: prisoner’s dilemmas, assurance games, chicken games, and coordination games. This paper aims to find a possible solution for Social dilemma. In this paper, we focus on a two-person social dilemma: Prisoner’s Dilemma and propose a contract which is negotiated by authorities to solve this problem. The contract says that the cooperators can be rewarded and the defectors will be punished. However, the player’s collective rationality will ultimately depend on their knowledge about the contract. By introducing the third person: a secretary whose task is to convey the contract to the players and who is completely truthful, we transform the two-player static game into a two-coalition dynamic game, one for the two-player and the other for secretary. In this new game, the secretary’s rationality tells her to perform the strategy ‘convey’, which will bring her better payoff than the strategy ‘not convey’, since the authorities will punish her seriously if she balks at the task. In addition, the secretary is completely truthful. Thus, once the two players, Bob and Jim, learn the contract from the secretary, they will realize that the cooperation is their best choice as a coalition after knowing that their previous payoffs would have been changed. After introducing the notion of knowledge-based cooperation, we offer an S5, history-based semantics proposed by Parikh and Ramanujam [PR03] to express this notion. These enable us to represent how the contract is transmitted between the two coalitions, and how their knowledge changes, which make the players perform the collective action. The contribution of our work is that we formalize the players’ reasoning in this new dynamic game and a semantic and axiomatic system is provided.

Cooperation of agents is a major issue in fields such as computer science, economics and philosophy. The conditions under which coalitions are formed occur in various situations involving multiple agents.

Various modal logic (ML) frameworks have been developed for reasoning about coalitional power; an important one is Coalition Logic (

CL

) [7], using modalities of the form 〈[

C

〉]

φ

saying “coalition

C

has a joint strategy to ensure that

φ

”.

CL

has neighborhood semantics but can be simulated on Kripke models [3]. Another class of cooperation logics explicitly represents the strategies and actions by which groups can achieve something [8].

In intuitionistic logic system, constructive negation operator complies with the law of contradiction but not the law of excluded middle in intuitionistic logic system.In da Costa’s paraconsistent logic system , paraconsistent negation operator complies with the law of excluded middle but not the law of contradiction. Putting aside classical negation operator, both intuitionistic logic and da Costa’s paraconsistent logic establish logic systems by directly introducing new negation operators basing on the positive proposition logic. This paper attempts to make constructive negation operator and paraconsistent negation operator satisfying the conditions mentioned above in classical logical system.

Oppositional logic is an extended system of classical propositional logic. It can be obtained from the classical propositional logic by adding an unary connective * and introducing the definitions of two unary connectives ∆ and ∇. In oppositional logic system, there are four kinds of negation: the classical negation ¬ complying with both law of contradiction and law of excluded middle, the constructive negation ∇ complying with law of contradiction but not law of excluded middle, the paraconsistent negation ∆ complying with law of excluded middle but not law of contradiction, as well as the dialectical negation * complying with neither law of contradiction nor law of excluded middle.

This paper gives the proof of the soundness and completenesstheorem of oppositional logic. It also gives the following conclusions:

[1] Oppositonal logic can be a kind of tools for paraconsistent theory and intuitionistic theory; the famous Duns Scotus law does not hold according to the paraconsistent negation and the dialectical negation;

[2] In oppositonal logic, according to the unary connective ¬, * , ∇ and ∆,

A

is in contradictory opposition with ¬

A

;

A

is in subaltern opposition with *

A

;

A

is in contrary opposition with ∇ 

A

;

A

is in subcontrary opposition with ∆ 

A

. In this sense, we call the logical system mentioned above oppositional logic.

Deliberate contrary-to-law action is a kind of action that caused by the inconsistent of law and personal intention. This kind of action is not encouraged, however, it offen happens in our society as a kind of irrational actions. In this paper I will use the theory of agents and choices to show that deliberate contrary-to-law action is not a kind of irrational actions. It is a pragmatic problem which can be interpreted by perspectival act utilitarianism. But perspectival act utilitarianism is based on decision theory especialy the theory of normative behavior. I think the theory of descirptive behavior is more suitable to interpret deliberate contrary-to-law action so I will alter some disciplines in John Hortys perspectival act utilitarianism to show why people do deliberate contrary-to-law action. The modified perspectival act utilitarianism can also be a kind of interpretation about irrational actions.

We model the information flow between different states of a single agent as that agent reasons deductively. K–axiom–based epistemic closure for explicit knowledge is rejected for even the most trivial cases of inferential reasoning on account of the fact that the closure axiom does not extend beyond a raw consequence relation.

The resource management of the database of agent states for the deductive reasoning fragment in question is covered by the logic corresponding to the

non–associative Lambek Calculus with permutation, bottom, and identity

:

NLP

0 , 1

.

The link between modal logic and non-well-founded sets has been shown by P. Aczel [1988], and systematically by J. Barwise and L. Moss [1996]. A. Baltag [1998] also proved some important theorems about characterizing sets by modal sentences. The aim of this paper is to explore the relationship between modal logic and sets more deeply in the expressive power of modal languages and modal definability over sets. Let’s consider both basic and infinitary modal languages.

Classical

Epistemic Logic

(

EL

) is a compact and powerful framework for representing an agent’s information. In its dynamic versions (

Dynamic Epistemic Logic

), it also describes the information flow driven by observation and communication. Nevertheless, it makes a strong idealization: the agent’s information is closed under logical consequence, making truth-preserving inference uninformative. This criticism extends to its dynamics versions: acts of observation and communication provides the agent not only with the new information but also with all logical consequences of it. Thus, dynamic epistemic logics lack of an account of the step-by-step information flow driven by agent’s inferences, a concern that arises not only in epistemic contexts, but also in doxastic areas. The extended version of the present abstract [1] combines ideas from the earlier literature proposing a unified framework to address these problems.

In social life of human being, individuals or collective group will be always confronted with choices. The occurring of choice implies that rational action agent (individual, collective group or social group in wide sense) must make a satisfying decision based on the alternatives set whose cardinal number is at least 2. Choice depends on preferences (Fishburn (1979)), so the nature of choice can be deemed to preference whether for individual or collective group. Preference is the ordering of alternatives given by rational agent according to his own will based on the sensibility and proneness. Preference can be crisp and fuzzy also.