Update README.md

Author: Alexander Steen

README.md

@@ -20,9 +20,9 @@ Currently, only modal logics are supported:
 | `$alethic_modal` | Same as `$modal` only that the operators are called `{$necessary}` and `{$possible}` instead (short forms are identical).  |
 | `$deontic` | Same as `$modal` only that the operators are called `{$obligatory}` and `{$permissible}` instead (short forms are identical).  |
 | `$alethic_modal` | Similar to `$modal` only that there is only one operator called `{$knows}` (short forms `[.]`).  |
-| `$$hybrid` | Hybrid logics extend the modal logic family $modal with the notion of nominals, a special kind of atomic formula symbol that is true only in a specific world [2]. The logics represented by $$hybrid are first-order variants of H(E, @, ↓). |
-| `$$pal` | Public announcement logic (PAL) is a propositional epistemic logic that allows for reasoning about knowledge. In contrast to $modal, PAL is a dynamic logic that supports updating the knowledge of agents via so-called announcement operators. |
-| `$$ddl` | Deontic logics are formalisms for reasoning over norms, obligations, permissions and prohibitions. In contrast to modal logics used for this purpose (e.g., modal logic D), dyadic deontic logics (DDLs), named $$ddl, offer a more sophisticated representation of conditional norms using a dyadic obligation operator O(ϕ/ψ). They address paradoxes of other deontic logics in the context of so-called contrary-to-duty (CTD) situations. The concrete DDLs supported are the propositional system by Carmo and Jones and Åqvist’s propositional system E. |
+| `$$hybrid` | Hybrid logics extend the modal logic family $modal with the notion of nominals, a special kind of atomic formula symbol that is true only in a specific world [2]. The logics represented by $$hybrid are first-order variants of H(E, @, ↓). A nominal symbol `n` is represented as `{$$nominal}(n)`, the shift operator @s as `{$$shift(#s)}`, and the bind operator ↓ x as `{$$bind(#X)}`. All other aspects are analogous to the modal logic representation above.|
+| `$$pal` | Public announcement logic (PAL) is a propositional epistemic logic that allows for reasoning about knowledge. In contrast to $modal, PAL is a dynamic logic that supports updating the knowledge of agents via so-called announcement operators. The knowledge operator Ki is given by `{$$knows(#i)}`, the common knowledge operator CA , with A a set of agents, by `{$$common($$group := [...])}`, and the announcement [!ϕ] is represented as `{$$announce($$formula := phi)}`. |
+| `$$ddl` | Deontic logics are formalisms for reasoning over norms, obligations, permissions and prohibitions. In contrast to modal logics used for this purpose (e.g., modal logic D), dyadic deontic logics (DDLs), named $$ddl, offer a more sophisticated representation of conditional norms using a dyadic obligation operator O(ϕ/ψ). They address paradoxes of other deontic logics in the context of so-called contrary-to-duty (CTD) situations. The concrete DDLs supported are the propositional system by Carmo and Jones and Åqvist’s propositional system E. The dyadic deontic operator O is represented by `{$$obl}` (short for obligatory). |
 
 ### Logic specifications
 Non-classical logic languages quite commonly admit different concrete logics using the same syntax. In order to chose the exact logic intended for the input