A conceptual system is a system that is composed of nonphysical objects, i.e. ideas or concepts. In this context a system is taken to mean "an interrelated, interworking set of objects".
Contents 
A conceptual system is simply a model. There are no limitations on this kind of model whatsoever except those of human imagination. If there is an experimentally verified correspondence between a conceptual system and a physical system then that conceptual system models the physical system. "values, ideas, and beliefs that make up every persons view of the world": that is a model of the world; a conceptual system that is a model of a physical system (the world). The person who has that model is a physical system.
In psychology and social work, when they talk about a conceptual system, they are referring to some person's model of the world, but if they try to understand that model, they end up making a model of that model, which is just a model of the person's behavior. In any case, this is exactly the purpose of the general term "conceptual systems".
The basis of all this is simple: the notion that something exists demands that the thing that exists be addressable. That is to say that there must be some observable or conceivable manifestation of the thing that is said to exist. If the manifestation is observable then the thing is a physical system (or object, it doesn't matter which for physical systems until you get down to indivisible particles). If the thing is not observable but is conceivable its a conceptual system.
More precisely: consider the set of all systems. Implicitly, the set of all objects is a subset of the set of all systems because a systems in an interacting structure of subsystems and/or objects. The set of all conceptual and the set of all physical systems are both subsets of this set. For higher precision, one may first consider the set of all valid properties, then allow every system to be defined as a binary string which encodes the truth value of every property applied to that object or system. In that way uniqueness is guaranteed and the system is paradox free (due to filtering the set of properties first).
In general the set of all conceptual systems is infinite. But it may be built up as a finite structure like a dictionary, only including the conceptual systems that are known, and adding new ones as they arise. Given the broadness of 'conceptual systems', the set of all conceptual systems would be uncountably infinite because every real number is a conceptual object.
Examples of conceptual systems are:
A concept is an abstract idea or a mental symbol, typically associated with a corresponding representation in and language or symbology, that denotes all of the objects in a given category or class of entities, interactions, phenomena, or relationships between them. Concepts are abstract in that they omit the differences of the things in their extension, treating them as if they were identical. They are universal in that they apply equally to every thing in their extension. Concepts are also the basic elements of propositions, much the same way a word is the basic semantic element of a sentence. Unlike perceptions, which are particular images of individual objects, concepts cannot be visualized. Because they are not, themselves, individual perceptions, concepts are discursive and result from reason. They can only be thought about, or designated, by means of a name. Words are not concepts. Words are signs for concepts.
A conceptual model is a representation of some phenomenon, data or theory by logical and mathematical objects such as functions, relations, tables, stochastic processes, formulas, axiom systems, rules of inference etc. A conceptual model has an ontology, that is the set of expressions in the model which are intended to denote some aspect of the modeled object. Here we are deliberately vague as to how expressions are constructed in a model and particularly what the logical structure of formulas in a model actually is. In fact, we have made no assumption that models are encoded in any formal logical system at all, although we briefly address this issue below. Moreover, the definition given here is oblivious about whether two expressions really should denote the same thing. Note that this notion of ontology is different from (and weaker than) ontology as is sometimes understood in philosophy; in our sense there is no claim that the expressions actually denote anything which exists physically or spatiotemporally (to use W. Quine's formulation).
For example, a stochastic model of stock prices includes in its ontology a sample space, random variables, the mean and variance of stock prices, various regression coefficients etc. Models of quantum mechanics in which pure states are represented as unit vectors in a Hilbert space include in their ontologies observables, dynamics, measurement operators etc. It is possible that observables and states of quantum mechanics are as physically real as the electrons they model, but by adopting this purely formal notion of ontology we avoid altogether this question.
A conceptual framework is used in research to outline possible courses of action or to present a preferred approach to a system analysis project. The framework is built from a set of concepts linked to a planned or existing system of methods, behaviors, functions, relationships, and objects. A conceptual framework might, in computing terms, be thought of as a relational model.
For example a conceptual framework of accounting "seeks to identify the nature, subject, purpose and broad content of generalpurpose financial reporting and the qualitative characteristics that financial information should possess".^{[1]}
