Public Key Encryption for Message Confidentiality In public-key encryption, if the decryption algorithm is
$$\text{Dec}(k_i,\text{Enc}(K_i,p))=p$$
where $k_i$ = receiver's private key and $K_i$ = receiver's public key
what would be the algorithm for encryption? Would it be
$$\text{Enc}(K_i,\text{Dec}(k_i,c))=c$$
Just looking for some clarification.
The question's formula $\text{Dec}(k_i,\text{Enc}(K_i,p))=p$ is for both encryption and decryption.
Encryption is $p\mapsto\text{Enc}(K_i,p)=c$.
Decryption is $c\mapsto\text{Dec}(k_i,c)=p$.
Note that $\text{Dec}$ can be a true function, but $\text{Enc}$ likely has a hidden random argument. Otherwise encryption would be deterministic, and deterministic encryption is vulnerable to chosen-message attack, especially public key encryption. If a name on the public class roll is encrypted with deterministic public-key encryption (such as textbook RSA encryption), anyone can find the name from the ciphertext, simply by enciphering all names on the class roll and comparing with the ciphertext.

In a textbook RSA context, $\text{Enc}(K_i,\text{Dec}(k_i,c))=c$ would be equivalent to textbook RSA signature of message $c$ followed by textbook RSA signature verification. But it is using a confusing notation, that won't work in most other signature contexts (e.g. Schnorr signature, DSA, ECDSA, EdDSA).