I guess that most of the time philosophers reason about properties and relations of variables that have finite number of possible values. For that specific case there is something very similar to truth tables for first order logic. So maybe you are looking for languages that are describing databases like ER-model, EER-model, relational model, relational algebra, UML and ORM. These languages essentially are first order logic for discrete variables. Databases feels somewhat like truth-tables-2.0.
Connection between databases, first order logic and truth tables.
You may be unsatisfied with thing that these languages deal with tables that are filled with text. If you like You can assign numbers to table names, field names and number all possible values in the table. So you'll get tables filled with natural numbers.
If you like you can obtain tables that contain the same information, but are filled with zeros or ones.
Aggregation ( in EER model) is somewhat similar to conjunction and disjunction, and arrow drawn from one table to other (in database schemas) somewhat similar to implication. Types of arrows somewhat resemble quantifiers.
When you reason about database, concepts from Relational algebra are very useful. Using Cartesian product and taking subset of it you can form relations.
Similarity between truth tables and databases.
Lets consider propositional logic example. You have some formula α(A,B,C). It has truth table. All formulas that have the same truth table are equivalent. Now imagine that all rows in truth table of α(A,B,C) that corresponds to α(A,B,C)=0 were deleted. This truth table without zero values of formula carries the same information as the original.
Similarly, imagine there are two database schemas, there is corresponding data base. If two schemas are equivalent than thy have the same database. Database schema consists of "tables" that are connected with arrows. These "tables" consist of name and list of fields (e.g. variables). So arrows connect fields of these "tables". So there is net of these tables connected with arrows. It is possible to obtain unique table for database. This can be done (if I remember correctly) by natural join operator.
Literature. You might be interested in Peters Chens work "English sentence structure and entity-relationship diagrams" and Sven Hartmanns work "English sentence structures and EER modeling".
I also like https://www.tutorialspoint.com/dbms/er_model_basic_concepts.htm.
I like Therrys Halpins book "Information modeling and relational databases".
These languages may seem mystic to you, but they are very easy if you find proper enterance point, so I suggest to start with data bases shemas, for example MS acess or LO base databases. I Like tutorials that are on https://www.thefrugalcomputerguy.com/ website.
Than you can start learning ER-model, than UML.