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«March 31, 2015 Abstract The term social software was coined by Rohit Parikh in 2002. Social soft- ware can be viewed as a research program which ...»

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A Non-Classical Logical Approach to Social


Can Baskent


University of Bath, England

www.canbaskent.net/logic, can@canbaskent.net

March 31, 2015


The term social software was coined by Rohit Parikh in 2002. Social soft-

ware can be viewed as a research program which studies the construction

and verification of social procedures by using tools in logic and computer

science. However, to the best of my knowledge, social software has not

been considered from a non-classical logical perspective. In this paper, I ar- gue how non-classical logical approaches can enrich, broaden and support the agenda of social software.

1 Introduction and Motivation The term social software was coined by Rohit Parikh in his 2002 paper (Parikh, 2002). Social software can be viewed as a research program which studies the construction and verification of social procedures by using tools in logic and computer science. By definition, it relates closely to a variety of neighboring fields including game theory, social choice theory and behavioral economics.

However, to the best of my knowledge, social software has not been considered from a non-classical logical perspective. In this paper, I argue how non-classical logical approaches can enrich, broaden and support the agenda of social soft- ware. Additionally, I will claim that incorporating non-classical elements to the program of social software aligns very well with its initial motivation.

Parikh himself does not seem to commit himself to the classical logic in the original paper, yet the de facto logic he utilizes in his work is classical. On the other hand, classical logic does not seem to be an essential element of the

program of social software:

I want to argue that (...) no doubt we shall never have social proce- dures which work ideally, we can nonetheless have a theory of social procedures which is analogous to the formal theories for computer 1 algorithms which exist in computer science. I am referring here to a whole group of theories, some of which have come into existence during the early seventies and some are newer.

(Parikh, 2002) I argue that the above quoted claim and, in general, the research program of social software, suggest the inclusion of formal tools beyond classical logic to study social software. Plurality of social procedures and their various anomalies (such as lies, jokes and speech acts) necessitate a pluralistic approach. More- over, truth gaps and truth gluts are ordinary parts of logical formalisms which can be used to give a formal account of a variety of social phenomena. In fact, this is one of the main motivations behind logical pluralism: classical Boolean logic suffers from various restrictions which render it rather problematic in explaining human behavior and reasoning. In some cases, we can have different notions of logical consequence; in some cases, we may need more truth values;

in some cases, we may have to reevaluate and redefine the logical connectives.

Furthermore, it is not entirely clear how exactly people reason in social situations, and to which logical framework they are usually committed (Kahneman, 2011).

In this work, in terms of logical pluralism and non-classical logics, I mainly focus on paraconsistent logics. I use the term paraconsistency for the logical systems in which the rule of explosion fails. In such systems, for some ϕ, ψ, we have ϕ, ¬ϕ ψ. In short, paraconsistent systems are the logical frameworks that allow non-trivial inconsistent theories where a trivial theory is a set of sentence from which everything logically follows. Paraconsistent logic, therefore, allows us build inconsistency-tolerant models. I believe this is a key notion in understanding social software.

There are various reasons for that. First of all, contradictions occur in social phenomena. People lie, cheat, make mistakes, and misunderstand each other, they happen to be wrong in their thoughts and actions, and all of these situations (and possibly many more) require an inconsistency-friendly framework for expressive power and normative predictions. Moreover, various data from behavioral economics indicate that people usually do not reason in the way that the classical logic predicts (Kahneman, 2011; Ariely, 2008; Ariely, 2010). This observation, by no means, entails that people always reason in a non-classical logical way. However, it casts doubt on the soundness of classical logical tools and encourages us to consider non-classical logical apparatus. Also, there can be found a variety of situations in social software that seem to fit well with non-classical logical reasoning. For instance, when people make an error in reasoning that can cause an inconsistency, the very existence of the inconsistency does not render the formalism trivial. People keep reasoning in their inconsistent model in a sound way. Sometimes they revise their beliefs, sometimes they reason non-monotonically, sometimes they ignore the inconsistency.

Yet, there also exist some other sort of inconsistencies in human reasoning and social procedures. Perhaps, a canonical example for such cases comes from normativity. The problem is how people should act under the presence of con

–  –  –

The source of contradictory obligations need not be different contracts, but may be one and the same contract. Of course, in practice it is rare for a contract per se to be blatantly inconsistent, but it is not unusual for a contract plus contingent circumstances to give someone inconsistent obligations. Suppose, for example, that I contract to do z under condition X, but refrain from doing z under condition Y. We may suppose that X and Y are events not under the control of the parties of the contract, and that there is no reasonable likelihood of X and Y both occurring. Suppose that, despite this, both do occur. Can I then be held in breach for whichever of the actions I do not perform?

(Priest, 2006, p. 183) The issue, raised by Priest here, has some ontological commitments to the contradictory co-existence of X and Y, and the philosophical implications of this situation go beyond the scope of the current article. Nevertheless, it shows that paraconsistent approach to social situations presents itself as an important perspective, and there seems to be no reason why it should not be included within the agenda of social software.

Another example of a contradictory situation comes from one of Parikh’s recent papers. In my opinion, the “Kitty Genovese” case that Parikh and his coauthors discussed illustrates similar concerns.

[I]n the Kew Gardens section of Queens, New York City, Catherine Genovese began the last walk of her life in the early morning hours of March 13, 1964. As she locked her car door, she took notice of a figure in the darkness walking towards her. She became immediately concerned as soon as the stranger began to follow her.

As she got of the car she saw me and ran, the man told the court later, I ran after her and I had a knife in my hand... I could run much faster than she could, and I jumped on her back and stabbed her several times, the man later told the cops.

Many neighbours saw what was happening, but no one called the police. Mr. Koshkin wanted to call the police but Mrs. Koshkin thought otherwise. I didnt let him, she later said to the press, I told him there must have been 30 calls already.

–  –  –

In this case, the classical logic oriented analysis that the authors suggested is of deontic and epistemic logical in nature. That is, the witnesses did not call the police, thus did not fulfill their moral duty as they did not possess the full information of the event and their agency in relation to each other. Simply put, witnesses thought that some other people might have called the police already. This analysis is plausible. Yet, some other analyses can also be given for the Genovese case underlining that people may behave inconsistently in a non-trivial way.

One of the descriptive analysis of the situation calls for a paraconsistent framework. It is assumed that the witnesses are morally obliged to call the police, and these moral obligations are generally assumed to be factual and truthful, and they must be fulfilled. Yet, they sometimes are not. Based on these

deontic presuppositions, this is what we have:

WitnessAMurder → Obliged(CallPolice), WitnessAMurder CallPolice

If we endorse modus ponens, and assume that moral obligations need to be fulfilled (that is if Obliged(CallPolice) → CallPolice), then we derive both CallPolice and ¬CallPolice which is contradictory and incoherent under the classical negation and consequence relation. As widely known, there are various ways to modalize the above formulation by using deontic operators that stand for obligations, yet we will not dwell on the matter by entering into deontic logical debates and their paradoxes here.

It should be noted that the paradoxical situation in this case is avoidable.

As the standard analysis for the Genovese example explicates, if the witnesses knew individually that none of the other witnesses called the police, they could have fulfilled their moral obligation.

Additionally, a simple game theoretical analysis of the situation can be considered. If a witness calls the police to report the incident, the cost to the witness for the call is less than a dollar and couple minutes which is by far negligible compared to the possible benefit that the call might bring about: saving the life of Kitty Genovese. Simply put, even if a moral agent i assumes that 1000 people saw the incident, and the chances that i will be the one who will report the incident first to the police is 0.1%, it is still the rational move to make, since a person’s life (nearly universally) is more valuable than the troubles that i needs to go through to report the incident - yielding a much higher expected utility for the call. Therefore, regardless of attaining the full knowledge of the case, I maintain that the witnesses have the obligation to the best of their knowledge to report the incident. Perhaps, they would be the 999th person to report it, which 4 is perfectly acceptable, but maybe they would be the first. Additional irregularities can also be the case in the Genovese example. For the legal authorities, receiving multiple calls for the same incident may backfire or perhaps can be ignored, and consequently trigger a higher cost for the individuals when they consider making the call. Moreover, as The New York Times article reporting the event quoted, witnesses were afraid to get involved and thought that it was a “lover’s quarrel”1. Such reasons are perfectly justifiable but may not rationally be the best move for not making the call. In either of these cases, game theoretical reasoning dictates that rational agents should make the call. Yet, they did not. Then, the classical analysis suggests that the agents in this case are not rational - perhaps excluding the ones with imperfect information. Paraconsistent analysis, on the other hand, prevents this over-reaching revision. It can very well be the case that agents could be perfectly rational (and most likely they were), had perfect information about the incident (they were the witnesses), yet they still did not make the call. Therefore, adopting a paraconsistent view point helps us construct a broader formal framework where we do not need to revise the initial assumptions of the theory just because an inconsistency occurred. In paraconsistent social software, we can very well have perfectly rational agents that can make mistakes. This simple example, in my opinion, argues that social software can easily allocate non-classical logics, and can be enriched by it. This seems as a powerful research direction within the domain of social software by extending the discussions on rationality, action-based models and utility theory.

The Kitty Genovese example and many others from law2 illustrate the possibility of applying non-classical logical methods to social software. The central claim of this paper is to argue that social software lies within the interesting intersection of logical, moral and economical pluralisms, and it can further benefit from incorporating non-classical logical methods into the theory. Additionally, apart from the descriptive perspective it provides, non-classical logical theories in social software can depict normative theories. In this work, we will not go into the details of this distinction.

In short, in order to analyze a variety of interesting social procedures and phenomena, we may need to use a variety of different logics. And social software, in all its richness, seems to provide an ideal domain to test the strengths (and weaknesses) of different formalisms. Similar to logical pluralism, I will argue for pluralism in social software, and this clearly falls within the agenda of social software as a research program. Rich formalisms in non-classical logics, the extensive research in behavioral economics and the way it discusses the pluralities in rational and social behavior, and finally alternative economic theories open up new avenues for social software and relate it to a broader audience.

I will argue for these points by suggesting a pluralistic framework - logically, morally and economically.

1 37Who Saw Murder Didn’t Call the Police, Martin Gansberg, The New York Times, 27.03.1965.

2A canonical example from law is civil disobedience where agents deliberately break the law and create an inconsistent situation where moral obligations and legal duties clash. Yet, still we obtain a non-trivial and coherent inconsistent situation.

5 2 A Broader Social Base for Social Software The recent rise of behavioral economics in both popular literature and academic research points out a well-known missing link between formal logic, and social and individual human behavior: people do not reason or behave as normatively as manifested by the classical logic. People often times make various deductions that diverge from the classical logic, hinting at the possibility of adopting logical pluralism to address the logic of society.

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