R. Nachman says that if someone denies a claim completely he must swear a Shevu'as Heses.
If a Ba'al ha'Bayis instructs a storekeeper to provide goods for his workers on credit and the workers claim they did not receive it and the storekeeper claims that he provided them they both swear and collect from the Ba'al ha'Bayis.
If a Shomer Chinam claims that the Pikadon was stolen he must swear three Shevu'os, that he was not negligent, that he didn't use the object and that it is not in his possession.
According to R. Yochanan a person who is suspected to steal money is not suspected to swear falsely.
Abaye says that if two people are holding a Talis and each one claims it belongs to them they must swear because maybe they are grabbing the Talis because they have a Safek that their friend owes them money for a loan. (1)
A person will not swear mi'Safek but he will take something that is not his mi'Safek since it is always possible to return it.
If two people are holding on to a Talis and one grabs it in front of Beis Din and the other is silent his silence is regarded as an admission. (2)
If two people are holding on to a Talis and Beis Din instructs them to split it and they come back with one of them in complete possession of the Talis and he claims the second person admitted that it is his and the second person claims that he rented it to him the first person is believed. (3)
If one person is holding a Talis and the second person is holding on to the edge of the Talis the Talis belongs to the first person. (4)
If two people are holding on to a Talis and one grabs it in front of Beis Din and the second person is silent and than he raises his voice it is a Safek if his initial silence is regarded as an admission
If the Halachah is that initial silence is not regarded as an admission if one of them is Makdish the Talis without grabbing it the Hekdesh is not effective.
If silence is regarded as an admission if one of them is Makdish the Talis without grabbing it is a Safek if the Hekdesh is effective.
A Safek Bechor whether it is a person or a Kosher or non-Kosher animal doesn't have to be given to a Kohen because Ha'Motzi me'Chaveiro Alav ha'Re'ayah. (5)
Although a Safek Bechorah doesn't have to be given to a Kohen it is forbidden to shear it or do work with it.
A Safek Pidyon Perter Chamor must be placed together with the animals that he is separating Ma'aser Beheimah from.
If a person is counting his animals in order to separate Ma'aser Beheimah and one of the animals that was already counted jumped back in to the pen and is mixed up among the animal all of the animals are Patur from Ma'aser. (6)
A BIT MORE
1. Abaye holds that a person who is suspected to steal is also suspected to swear falsely and therefore he says that we don't suspect that he is stealing the Talis but rather that he thinks that maybe the person woes him money and he is taking the Talis as payment.
2. However if he raises his voice when his friend grabs it the Din is unchanged and they both swear and take half.
2. We believe him that the second person admitted that it is his because he would not have rented it to him without witnesses since he originally claimed that he stole it from him.
4. Even according to Sumchus who holds that money which is a Safek is divided between them without a Shevu'ah would agree that the person holding the edge of the Talis doesn't get anything because holding on to the edge is of no consequence.
5. An example of a Safek Bechor is if the mother previously miscarried and we have a Safek if the miscarried offspring was developed enough to Patur a subsequent born offspring from Bechorah.
6. it is a Gezeiras ha'Kasuv that an animal that has been counted even if the count was never completed is Patur from Ma'aser and when one of the counted animals gets mixed in with the other animals all of the animals are Patur mi'Safek.