Parameter type covariance in specializations

Question

tl;dr

What strategies exist to overcome parameter type invariance for specializations, in a language (PHP) without support for generics?

_{Note: I wish I could say my understanding of type theory/safety/variance/etc., was more complete; I'm no CS major.}

Situation

You've got an abstract class, Consumer, that you'd like to extend. Consumer declares an abstract method consume(Argument $argument) which needs a definition. Shouldn't be a problem.

Problem

Your specialized Consumer, called SpecializedConsumer has no logical business working with every type of Argument. Instead, it should accept a SpecializedArgument (and subclasses thereof). Our method signature changes to consume(SpecializedArgument $argument).

abstract class Argument { }

class SpecializedArgument extends Argument { }

abstract class Consumer { 
    abstract public function consume(Argument $argument);
}

class SpecializedConsumer extends Consumer {
    public function consume(SpecializedArgument $argument) {
        // i dun goofed.
    }
}

We're breaking Liskov substitution principle, and causing type safety problems. Poop.

Question

Ok, so this isn't going to work. However, given this situation, what patterns or strategies exist to overcome the type safety problem, and the violation of LSP, yet still maintain the type relationship of SpecializedConsumer to Consumer?

I suppose it's perfectly acceptable that an answer can be distilled down to "ya dun goofed, back to the drawing board".

Considerations, Details, & Errata

Alright, an immediate solution presents itself as "don't define the consume() method in Consumer". Ok, that makes sense, because method declaration is only as good as the signature. Semantically though the absence of consume(), even with a unknown parameter list, hurts my brain a bit. Perhaps there is a better way.
From what I'm reading, few languages support parameter type covariance; PHP is one of them, and is the implementation language here. Further complicating things, I've seen creative "solutions" involving generics; another feature not supported in PHP.
From Wiki's Variance (computer science) - Need for covariant argument types?:

This creates problems in some situations, where argument types should be covariant to model real-life requirements. Suppose you have a class representing a person. A person can see the doctor, so this class might have a method virtual void Person::see(Doctor d). Now suppose you want to make a subclass of the Person class, Child. That is, a Child is a Person. One might then like to make a subclass of Doctor, Pediatrician. If children only visit pediatricians, we would like to enforce that in the type system. However, a naive implementation fails: because a Child is a Person, Child::see(d) must take any Doctor, not just a Pediatrician.

The article goes on to say:

In this case, the visitor pattern could be used to enforce this relationship. Another way to solve the problems, in C++, is using generic programming.

Again, generics can be used creatively to solve the problem. I'm exploring the visitor pattern, as I have a half-baked implementation of it anyway, however most implementations as described in articles leverage method overloading, yet another unsupported feature in PHP.

Implementation

Due to recent discussion, I'll expand on the specific implementation details I've neglected to include (as in, I'll probably include way too much).

_{For brevity, I've excluded method bodies for those which are (should be) abundantly clear in their purpose. I've tried to keep this brief, but I tend to get wordy. I didn't want to dump a wall of code, so explanations follow/precede code blocks. If you have edit privileges, and want to clean this up, please do. Also, code blocks aren't copy-pasta from a project. If something doesn't make sense, it might not; yell at me for clarification.}

With respect to the original question, hereafter the Rule class is the Consumer and the Adapter class is the Argument.

The tree-related classes are comprised as follows:

abstract class Rule {
    abstract public function evaluate(Adapter $adapter);
    abstract public function getAdapter(Wrapper $wrapper);
}

abstract class Node {
    protected $rules = [];
    protected $command;
    public function __construct(array $rules, $command) {
        $this->addEachRule($rules);
    }
    public function addRule(Rule $rule) { }
    public function addEachRule(array $rules) { }
    public function setCommand(Command $command) { }
    public function evaluateEachRule(Wrapper $wrapper) {
        // see below
    }
    abstract public function evaluate(Wrapper $wrapper);
}

class InnerNode extends Node {
    protected $nodes = [];
    public function __construct(array $rules, $command, array $nodes) {
        parent::__construct($rules, $command);
        $this->addEachNode($nodes);
    }
    public function addNode(Node $node) { }
    public function addEachNode(array $nodes) { }
    public function evaluateEachNode(Wrapper $wrapper) {
        // see below
    }
    public function evaluate(Wrapper $wrapper) {
        // see below
    }
}

class OuterNode extends Node {
    public function evaluate(Wrapper $wrapper) {
        // see below
    }
}

So each InnerNode contains Rule and Node objects, and each OuterNode only Rule objects. Node::evaluate() evaluates each Rule (Node::evaluateEachRule()) to a boolean true. If each Rule passes, the Node has passed and it's Command is added to the Wrapper, and will descend to children for evaluation (OuterNode::evaluateEachNode()), or simply return true, for InnerNode and OuterNode objects respectively.

As for Wrapper; the Wrapper object proxies a Request object, and has a collection of Adapter objects. The Request object is a representation of the HTTP request. The Adapter object is a specialized interface (and maintains specific state) for specific use with specific Rule objects. (this is where the LSP problems come in)

The Command object is an action (a neatly packaged callback, really) which is added to the Wrapper object, once all is said and done, the array of Command objects will be fired in sequence, passing the Request (among other things) in.

class Request { 
    // all teh codez for HTTP stuffs
}

class Wrapper {
    protected $request;
    protected $commands = [];
    protected $adapters = [];
    public function __construct(Request $request) {
        $this->request = $request;
    }
    public function addCommand(Command $command) { }
    public function getEachCommand() { }
    public function adapt(Rule $rule) {
        $type = get_class($rule);
        return isset($this->adapters[$type]) 
            ? $this->adapters[$type]
            : $this->adapters[$type] = $rule->getAdapter($this);
    }
    public function commit(){
        foreach($this->adapters as $adapter) {
            $adapter->commit($this->request);
        }
    }
}

abstract class Adapter {
    protected $wrapper;
    public function __construct(Wrapper $wrapper) {
        $this->wrapper = $wrapper;
    }
    abstract public function commit(Request $request);
}

So a given user-land Rule accepts the expected user-land Adapter. If the Adapter needs information about the request, it's routed through Wrapper, in order to preserve the integrity of the original Request.

As the Wrapper aggregates Adapter objects, it will pass existing instances to subsequent Rule objects, so that the state of an Adapter is preserved from one Rule to the next. Once an entire tree has passed, Wrapper::commit() is called, and each of the aggregated Adapter objects will apply it's state as necessary against the original Request.

We are then left with an array of Command objects, and a modified Request.

What the hell is the point?

Well, I didn't want to recreate the prototypical "routing table" common in many PHP frameworks/applications, so instead I went with a "routing tree". By allowing arbitrary rules, you can quickly create and append an AuthRule (for example) to a Node, and no longer is that whole branch accessible without passing the AuthRule. In theory (in my head) it's like a magical unicorn, preventing code duplication, and enforcing zone/module organization. In practice, I'm confused and scared.

Why I left this wall of nonsense?

Well, this is the implementation for which I need to fix the LSP problem. Each Rule corresponds to an Adapter, and that ain't good. I want to preserve the relationship between each Rule, as to ensure type safety when constructing the tree, etc., however I can't declare the key method (evaluate()) in the abstract Rule, as the signature changes for subtypes.

On another note, I'm working on sorting out the Adapter creation/management scheme; whether it is the responsibility of the Rule to create it, etc.