Dialogical logic

Dialogical logic is an approach towards logic into which some constants like quantifiers, connectives and validity notion get conveyed in terms of game-theory type of argument. These logical constants include words such as "and, not, imply, or and every" among many others. Their meanings get displayed in a manner that the assertions containing them can be defended or attacked when in an adversarial dialogue. These dialogues are known as two-player games since they occur between an opponent and proponent. Beginning with this dialogical logic, a proponent must make his/her assertion. It can, therefore, get attacked by an opponent depending on its logicality. Once the opponent has made their move, the proponent can consequently decide to defend or attack depending on the other party's response. The dialogue only comes to an end when the two participants have alternated in supporting their arguments until one is unable to make any more moves. The person who makes the last move is considered to have won that particular dialogue. The validity of proponent's initial assertion wins if they are able to successfully win every discussion representing the moves made by the opponent. If the initial argument fails to display logical defense, then the opponent succeeds in proving its invalidity. Therefore, it can be concluded that dialogical logic is the type of arguments conveyed between two parties where one side wins through presenting an undisputed move.

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Constituents of Dialogical Logic

Argumentation forms

It is responsible for giving logical constants like "implies" and "or" their meaning in dialogue. It is responsible for describing the two possible moves, which are defense and attack. The argumentation form helps determine precisely how opponent and proponent can use logical constants in their primary positions. Using the example of a logical constant "implies", it can be deduced that when one player asserts A, he or she implies B.

Therefore, in return, the other participant can attack this notion by arguing for A, which leads the first player to make his/her defense by claiming B. According to this understanding, one can confidently familiarize it with everyday dialogues. When an individual arguing for A implies B, they must be able to defend the B if granted A.

Dialogues

This is a single game where two players, namely proponent and opponent, participate. The first insertion is made by the proponent, who is mostly on the defensive side during the argument. Dialogues occur when these two parties alternate moves as each share their views on the topic under discussion. Every step taken is usually according to argumentation form used; however, there are conditions traditionally laid down at the beginning of each argument. Some of the rules implied are once a defense has been made against each attack, it cannot be repeated elsewhere. Some of these guidelines are bound to affect both players, while others are only imposed on one party. In such restriction rules, there is one that implies that a statement without logical constant can only be permitted for the proponent if his/her opponent has already asserted it. However, the opposing party has the freedom to insert this type of statement without any prohibition as long as argumentation form used allows it.

Winning strategy

For any player to win the dialogue, their assertions must be valid and provable. One cannot make a statement out of assumptions expecting it to win an argument. Such allegations can be faced with opposition hence not considered as winning strategies. In a dialogical logic, a statement can get regarded as valid if the proponent can have a plan for winning through it. It should be able to provide success for this player regardless of any moves made by the opponent. Winning strategies for proponents through assertions depend on conditions that determine the kind of dialogue being played. The validity of arguments depends on the types of rules imposed on individual dialogue games. Hence, ones these rules are changed, notions of validity could also become diverse into classical or intuitionist logic.

History and Development of Dialogical Logic

The semantics of dialogical logic was first introduced in the 1950s by mathematician and philosopher Paul Lorenzen. He used to call this type of argument "games for logic", and his notion was later developed by one of his student Kuno Lorenz. Since the 1950s, there has been a lot of studies on the semantics of games conducted concerning logic. In 1993, dialogic was studied by Shahid Rahman and his colleagues to determine its philosophical and logical issues. Currently, philosophers are venturing in fields of legal reasoning, argumentation theory, applied linguistics, computer science and artificial intelligence, among others.

The work of Jean-Yves Girard that focused on interaction and logic was one-sided as other philosophers like Samson Abramsky and Andreas Blass studied different dimensions like mathematical game theory and logical reasoning. All this research was conducted to show that dialogical interactions are a game based following new valid perspectives. They were also able to describe logic as dynamic inference instrument. There are research programs that can be identified today to have addressed the meaning of philosophy in dialogues as game interactions.

Literature Review on Dialogical Logic

According to Rahma Shahid and his associates, dialogical approach reasoning is not just a logical system. Contrary, they described it as a general framework whose meaning is controlled by rules. The approach allowed for the development of different logics which would form a basis for combination or comparison. Its central ideology states that argumentative interactions are made between epistemic subjects. The approach has remained constant throughout the history of logic and philosophy. These philosophers try to show what a dialogical framework can achieve in arguments between two players. Their approach considers opposition and proposition parties of an interaction.

From the research by Mattieu Fontaine and Cristina Barez Gomez, one can see how reasoning reconciles formal logic and argumentation theory. Agent-centred theory studies inferences as human activities that trigger an individual capacity to be rational. Therefore, no argument can be treated as independent of human activity, whether it gets conducted in deductive or non-deductive reasoning. According to these authors, dialogical logic occurs as argumentative games which gave agents with commitments and actions. In this ideology, an interaction starts with the proposition of a concession problem. Later, this issue presented gets opposed leading to an argument by these two parties.

Mathieu Beirlaen and Mattieu Fontaine explained that despite any inconveniences presented, good and bad arguments can be easily distinguished. There is an inconsistency-adaptive approach that helps make the distinction hence balancing between inferential strength and inconsistency-tolerance. According to these authors, they use Baten's method in conjunction with developmental of dialogical logic by Carnielli and Rahman. When these two frameworks are connected, a dynamic mechanism is generated that shows that inconsistencies get created when two parties share their opinions over a central issue. There are limited chances that two individuals arguing about a similar claim can end up in agreement. Most argumentative dialogues are as a result of diverse ideologies.

Four Research Programs of Dialogical Logic

Constructivism approach

Paul Lorenzen with Kuno Lorenz, tried to overcome operative logic shortcomings by assigning some dialogical foundations to it. In 1955, there was a semantic tableaux method for intuitionistic and classical logic introduced by Evert W Beth that could work best as a winning strategy in specific game based dialogues. The technique got expanded later by Rahman Shahid and his collaborators in the classical and non-classical studies. Rahma and his allies tried to come up with a dialogue rich in argumentive content. They found out that such could be achieved through a combination of the dialogical framework and interpretive language.

Game-theoretical approach

The dialogical notion was from Jaakko Hintikka and it was called GTS. The approach shares tenets of game-theoretic for logical constants. When the analysis of dialogical logic reaches an introductory statement level, it turns to standard model theory. When using this analysis method, the semantics of truth-function are engaged. One player in this formal play will end up losing his/her argument during negotiations.

In most cases, the defender portrays a lot of validity and provability hence winning the argument. Recently, a group of Amsterdam researchers led by Johan Van Benthem have launched more developments on this game-theoretical approach. They have managed to combine epistemic logic with game logic making them become considered as most dynamic in this field of research.

Argumentation theory approach

It was formulated in 1982 by Erik Krabbe and Else Barth. The approach tried to link critical reasoning with dialogical logic. Using informal logic in game-based arguments originated from Chaim Perelman in 1958, Charles Hamblin in 1970 and was further developed by Doughlas Walton in 1984 and Ralph Johnson in 1999 with other associates. The ideology continues to get extended with new perspectives being put in play by different philosophers.

The Ludics approach

The philosopher Jean Yves Girard incepted the approach. It was based on the theory of proofing meaning in player's statements. It is also based on interactive computing which highly regards validity. When one is making an argument, they must incorporate provable reasoning that an opponent can understand. Dialogical perspectives depict that social interactions help unleash knowledge and meaning of dialogues. These notions of truth and wisdom help form the arguments normalcy. Therefore, the right to ask questions and receive responses is what gives interaction with the understanding it needs between two players. To be able to prove the meaning of a statement, an opponent must ask questions to be answered by his/her proponent. They exchange vital knowledge that helps one to assert their moves appropriately.

Real-Life Comparison

In the case of a divorce, there are two parties involved that form the basis of an argument. These individuals have different points of view about their marriage which can only be solved by a game based discussion. When one individual acts as the proponent, he or she must be the one indeed of this procedure while the other acts as an opponent. They must be able to present individuals arguments which are to be faced with questions from either side. These people seeking a divorce can end up finalizing it or remaining married, considering which team wins. If the proponent conveys better argument than the opponent, his or her wish will get granted and the vice versa applies.

Most debates convey the settings of dialogical logic. In every situation, two sides have contrasting opinions. To settle this, they argue it out by both addressing their perspectives. Each party has its chances to make a move. They alternate until a winner is declared. The participant that gives a finale statement becomes the winner. Therefore, this notion can be sued to settle real-life situations.

Conclusion

Dialogical logic is meant to be a procedure where one party wins while the other loses. There are limited chances that both players could end up winners since the game concludes when the last person to argue makes the other incapable of giving more assertions. Most discussions in everyday settings work similarly to dialogical logic. Individuals converse or interact through debates and arguments. At the end of these social...