science

HiLog

HiLog is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand HiLog rather than just read about it. In short: HiLog is a programming logic with higher-order syntax, which allows arbitrary terms to appear in predicate and function positions. However, the model theory of HiLog is first-order.

Key takeaways

HiLog belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect HiLog to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of HiLog from memory before moving on to harder problems.

Reference excerpt

HiLog is a programming logic with higher-order syntax, which allows arbitrary terms to appear in predicate and function positions. However, the model theory of HiLog is first-order. Although syntactically HiLog strictly extends first order logic, HiLog can be embedded into this logic. HiLog was first described in 1989. It was later extended in the direction of many-sorted logic. The XSB system parses HiLog syntax, but the integration of HiLog into XSB is only partial. In particular, HiLog is not integrated with the XSB module system. A full implementation of HiLog is available in the Flora-2 system. It has been shown that HiLog can be embedded into first-order logic through a fairly simple transformation. For instance, p(X)(Y,Z(V)(W)) gets embedded as the following first-order term: apply(p(X),Y,apply(apply(Z,V),W)). The Framework for Logic-Based Dialects (RIF-FLD) of the Rule Interchange Format (RIF) is largely based on the ideas underlying HiLog and F-logic.

Examples In all the examples below, capitalized symbols denote variables and the comma denotes logical conjunction, as in most logic programming languages. The first and the second examples show that variables can appear in predicate positions. Predicates can even be complex terms, such as closure(P) or maplist(F) below. The third example shows that variables can also appear in place of atomic formulas, while the fourth example illustrates the use of variables in place of function symbols. The first example defines a generic transitive closure operator, which can be applied to an arbitrary binary predicate. The second example is similar. It defines a LISP-like mapping operator, which applies to an arbitrary binary predicate. The third example shows that the Prolog meta-predicate call/1 can be expressed in HiLog in a natural way and without the use of extra-logical features. The last example defines a predicate that traverses arbitrary binary trees represented as first-order terms.

References

Further reading Ross, Kenneth A. (January 1994). "On negation in HiLog". Journal of Logic Programming. 18 (1): 27–53. doi:10.1016/0743-1066(94)90040-X. Bruijn, Jos; Heymans, Stijn (January 2008). "On the relationship between description logic-based and F-logic-based ontologies". Fundamenta Informaticae. 82 (3): 213–236.

Worked examples

Example 1 — a first encounter with HiLog

Start with the simplest possible case. Write down what HiLog claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to HiLog before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about HiLog ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of HiLog

In research: HiLog appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses HiLog in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: HiLog is common in secondary-school and first-year university syllabi. It links to neighbouring topics Declarative programming languages, Knowledge representation, Logic programming languages, so understanding it makes those chapters shorter.
In everyday life: Look for HiLog outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study HiLog in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what HiLog means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain HiLog out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is HiLog in simple terms?

HiLog is a programming logic with higher-order syntax, which allows arbitrary terms to appear in predicate and function positions. However, the model theory of HiLog is first-order.

Why does HiLog matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study HiLog?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on HiLog.