Schema.org properties "logo", "mainEntityOfPage", "dateModified" give error in Google SDTT

Question

Following a tutorial I integrated the structured data in my WordPress website but when I run the google sd testing tool I continue to get an error that I can not fix on the logo and other minor things.

Here is my code (for what regards the "Article").

  $payload["@type"] = "Article";
  $payload["url"] = $post_url;
  $payload["author"] = array(
      "@type" => "Person",
      "name" => $author_data->display_name,
      );
  $payload["headline"] = $post_data->post_title;
  $payload["datePublished"] = $post_data->post_date;
  list($width, $height) = getimagesize( $post_thumb );
  $payload["image"] = array(
  "@type" => "ImageObject",
  "url" => $post_thumb,
  "height" => "350",
  "width" => "590");
  $payload["ArticleSection"] = $category[0]->cat_name;
  $payload["Publisher"] = "MyWebsite";

All works good but I got this error/warnings:

logo: mancante e obbligatorio (missing and required
dateModified: mancante e consigliato (Missing and recommended)
mainEntityOfPage: mancante e consigliato (Missing and recommended)

Can someone suggest me how to complete my code?

Answer 1

It seems that Google has recently changed the requirements for Article rich snippets.

See this link for more information : https://productforums.google.com/forum/#!topic/webmasters/ltbw0gUvReM

And this one for documentation : https://developers.google.com/structured-data/rich-snippets/articles#article_markup_properties

Hope it helps.

Edit for logo :

Follow this link to know how to set up the logo : http://schema.org/logo