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In artificial intelligence, the frame problem describes an issue with using First Order Logic (FOL) to express facts about a robot in the world. Representing the state of a robot with traditional FOL requires the use of many axioms that simply imply that things in the environment don't change arbitrarily. For example, Hayes describes a blocks world with rules about putting blocks on top of each other. In a FOL system additional axioms are required to infer facts such as a block does not change position if it's not moved. The frame problem is the problem of finding adequate collections of axioms for a viable description of a robot environment.^[1]

John McCarthy and Patrick J. Hayes defined this problem in their 1969 article, Some Philosophical Problems from the Standpoint of Artificial Intelligence. In this paper and many that came after the formal mathematical problem was a starting point for more general discussions of the difficulty of knowledge representation for artificial intelligence. Issues such as how to provide rational default assumptions and what humans consider common sense in a virtual environment.^[2] Later, the term acquired a broader meaning in philosophy, where it is formulated as the problem of limiting the beliefs that have to be updated in response to actions. In the logical context, actions are typically specified by what they change, with the implicit assumption that everything else (the frame) remains unchanged.

The frame problem in artificial intelligence

The frame problem occurs even in very simple domains. A scenario with a door, which can be open or closed, and a light, which can be on or off, is statically represented by two propositions $open$ and $on$ . If these conditions can change, they are better represented by two predicates $open (t)$ and $on (t)$ that depend on time; such predicates are called fluents. A domain in which at time 0 the door is closed, the light is off, and the door is opened at time 1 can be directly represented in logicTemplate:Clarify by the following formulae:

\neg open (0)

\neg on (0)

true \to open (1)

The first two formulae represent the initial situation; the third formula represents the effect of executing the action of opening the door at time 1. If such an action had preconditions, such as the door must not be locked, it would have been represented by $\neg locked (0) \to open (1)$ . In practice, one would have a predicate $executeopen (t)$ for specifying when an action is executed and a rule $\forall t . executeopen (t) \land true \to open (t + 1)$ for specifying the effects of actions. The article on the situation calculus gives more details.

While the three formulae above are a direct expression in logic of what is known, they do not suffice to correctly draw consequences. While the following conditions (representing the expected situation) are consistent with the three formulae above, they are not the only ones.

$\neg open (0)$	$open (1)$
$\neg on (0)$	$\neg on (1)$

Indeed, another set of conditions that is consistent with the three formulae above is:

$\neg open (0)$	$open (1)$
$\neg on (0)$	$on (1)$

The frame problem is that specifying only which conditions are changed by the actions do not allow, in logic, to conclude that all other conditions are not changed. This problem can be solved by adding the so-called “frame axioms”, which explicitly specify that all conditions not affected by actions are not changed while executing that action. For example, since the action executed at time 0 is that of opening the door, a frame axiom would state that the status of the light does not change from time 0 to time 1:

on (0) \leftrightarrow on (1)

The frame problem is that one such frame axiom is necessary for every pair of action and condition such that the action does not affect the condition.Template:Clarify In other words, the problem is that of formalizing a dynamical domain without explicitly specifying the frame axioms.

The solution proposed by McCarthy to solve this problem involves assuming that a minimal amount of condition changes have occurred; this solution is formalized using the framework of circumscription. The Yale shooting problem, however, shows that this solution is not always correct. Alternative solutions were then proposed, involving predicate completion, fluent occlusion, successor state axioms, etc.; they are explained below. By the end of the 1980s, the frame problem as defined by McCarthy and Hayes was solvedTemplate:Clarify. Even after that, however, the term “frame problem” was still used, in part to refer to the same problem but under different settings (e.g., concurrent actions), and in part to refer to the general problem of representing and reasoning with dynamical domains.

Solutions to the frame problem

In the following, how the frame problem is solved in various formalisms is shown. The formalisms themselves are not presented in full: what is presented are simplified versions that are however sufficient to show how the frame problem is solved.

The fluent occlusion solution

This solution was proposed by Erik Sandewall, who also defined a formal language for the specification of dynamical domains; therefore, such a domain can be first expressed in this language and then automatically translated into logic. In this article, only the expression in logic is shown, and only in the simplified language with no action names.

The rationale of this solution is to represent not only the value of conditions over time, but also whether they can be affected by the last executed action. The latter is represented by another condition, called occlusion. A condition is said to be occluded in a given time point if an action has been just executed that makes the condition true or false as an effect. Occlusion can be viewed as “permission to change”: if a condition is occluded, it is relieved from obeying the constraint of inertia.

In the simplified example of the door and the light, occlusion can be formalized by two predicates $occludeopen (t)$ and $occludeon (t)$ . The rationale is that a condition can change value only if the corresponding occlusion predicate is true at the next time point. In turn, the occlusion predicate is true only when an action affecting the condition is executed.

\neg open (0)

\neg on (0)

true \to open (1) \land occludeopen (1)

\forall t . \neg occludeopen (t) \to (open (t - 1) \leftrightarrow open (t))

\forall t . \neg occludeon (t) \to (on (t - 1) \leftrightarrow on (t))

In general, every action making a condition true or false also makes the corresponding occlusion predicate true. In this case, $occludeopen (1)$ is true, making the antecedent of the fourth formula above false for $t = 1$ ; therefore, the constraint that $open (t - 1) \leftrightarrow open (t)$ does not hold for $t = 1$ . Therefore, $open$ can change value, which is also what is enforced by the third formula.

In order for this condition to work, occlusion predicates have to be true only when they are made true as an effect of an action. This can be achieved either by circumscription or by predicate completion. It is worth noticing that occlusion does not necessarily imply a change: for example, executing the action of opening the door when it was already open (in the formalization above) makes the predicate $occludeopen$ true and makes $open$ true; however, $open$ has not changed value, as it was true already.

The predicate completion solution

This encoding is similar to the fluent occlusion solution, but the additional predicates denote change, not permission to change. For example, $changeopen (t)$ represents the fact that the predicate $open$ will change from time $t$ to $t + 1$ . As a result, a predicate changes if and only if the corresponding change predicate is true. An action results in a change if and only if it makes true a condition that was previously false or vice versa.

\neg open (0)

\neg on (0)

\neg open (0) \land true \to changeopen (0)

\forall t . changeopen (t) \leftrightarrow (\neg open (t) \leftrightarrow open (t + 1))

\forall t . changeon (t) \leftrightarrow (\neg on (t) \leftrightarrow on (t + 1))

The third formula is a different way of saying that opening the door causes the door to be opened. Precisely, it states that opening the door changes the state of the door if it had been previously closed. The last two conditions state that a condition changes value at time $t$ if and only if the corresponding change predicate is true at time $t$ . To complete the solution, the time points in which the change predicates are true have to be as few as possible, and this can be done by applying predicate completion to the rules specifying the effects of actions.

The successor state axioms solution

The value of a condition after the execution of an action can be determined by the fact that the condition is true if and only if:

the action makes the condition true; or
the condition was previously true and the action does not make it false.

A successor state axiom is a formalization in logic of these two facts. For example, if $opendoor (t)$ and $closedoor (t)$ are two conditions used to denote that the action executed at time $t$ was to open or close the door, respectively, the running example is encoded as follows.

\neg open (0)

\neg on (0)

opendoor (0)

\forall t . open (t + 1) \leftrightarrow opendoor (t) \lor (open (t) \land \neg closedoor (t))

This solution is centered around the value of conditions, rather than the effects of actions. In other words, there is an axiom for every condition, rather than a formula for every action. Preconditions to actions (which are not present in this example) are formalized by other formulae. The successor state axioms are used in the variant to the situation calculus proposed by Ray Reiter.

The fluent calculus solution

The fluent calculus is a variant of the situation calculus. It solves the frame problem by using first-order logic terms, rather than predicates, to represent the states. Converting predicates into terms in first order logic is called reification; the fluent calculus can be seen as a logic in which predicates representing the state of conditions are reified.

The difference between a predicate and a term in first order logic is that a term is a representation of an object (possibly a complex object composed of other objects), while a predicate represents a condition that can be true or false when evaluated over a given set of terms.

In the fluent calculus, each possible state is represented by a term obtained by composition of other terms, each one representing the conditions that are true in state. For example, the state in which the door is open and the light is on is represented by the term $open \circ on$ . It is important to notice that a term is not true or false by itself, as it is an object and not a condition. In other words, the term $open \circ on$ represent a possible state, and does not by itself mean that this is the current state. A separate condition can be stated to specify that this is actually the state at a given time, e.g., $state (open \circ on, 10)$ means that this is the state at time $10$ .

The solution to the frame problem given in the fluent calculus is to specify the effects of actions by stating how a term representing the state changes when the action is executed. For example, the action of opening the door at time 0 is represented by the formula:

state (s \circ open, 1) \leftrightarrow state (s, 0)

The action of closing the door, which makes a condition false instead of true, is represented in a slightly different way:

state (s, 1) \leftrightarrow state (s \circ open, 0)

This formula works provided that suitable axioms are given about $state$ and $\circ$ , e.g., a term containing two times the same condition is not a valid state (for example, $state (open \circ s \circ open, t)$ is always false for every $s$ and $t$ ).

The event calculus solution

The event calculus uses terms for representing fluents, like the fluent calculus, but also has axioms constraining the value of fluents, like the successor state axioms. In the event calculus, inertia is enforced by formulae stating that a fluent is true if it has been true at a given previous time point and no action changing it to false has been performed in the meantime. Predicate completion is still needed in the event calculus for obtaining that a fluent is made true only if an action making it true has been performed, but also for obtaining that an action had been performed only if that is explicitly stated.

The default logic solution

The frame problem can be thought of as the problem of formalizing the principle that, by default, "everything is presumed to remain in the state in which it is" (Leibniz, "An Introduction to a Secret Encyclopædia", c. 1679). This default, sometimes called the commonsense law of inertia, was expressed by Raymond Reiter in default logic:

\frac{R (x, s) : R (x, do (a, s))}{R (x, do (a, s))}

(if $R (x)$ is true in situation $s$ , and it can be assumed^[3] that $R (x)$ remains true after executing action $a$ , then we can conclude that $R (x)$ remains true).

Steve Hanks and Drew McDermott argued, on the basis of their Yale shooting example, that this solution to the frame problem is unsatisfactory. Hudson Turner showed, however, that it works correctly in the presence of appropriate additional postulates.

The answer set programming solution

The counterpart of the default logic solution in the language of answer set programming is a rule with strong negation:

r (X, T + 1) \leftarrow r (X, T), not \sim r (X, T + 1)

(if $r (X)$ is true at time $T$ , and it can be assumed that $r (X)$ remains true at time $T + 1$ , then we can conclude that $r (X)$ remains true).

Action description languages

Action description languages elude the frame problem rather than solving it. An action description language is a formal language with a syntax that is specific for describing situations and actions. For example, that the action $opendoor$ makes the door open if not locked is expressed by:

opendoor

causes

open

if

\neg locked

The semantics of an action description language depends on what the language can express (concurrent actions, delayed effects, etc.) and is usually based on transition systems.

Since domains are expressed in these languages rather than directly in logic, the frame problem only arises when a specification given in an action description logic is to be translated into logic. Typically, however, a translation is given from these languages to answer set programming rather than first-order logic.

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

J. McCarthy and P. J. Hayes (1969). Some philosophical problems from the standpoint of artificial intelligence. Machine Intelligence, 4:463-502.

E. Sandewall (1972), An approach to the Frame Problem and its Implementation, Machine Intelligence, 7:195–204.

J. McCarthy (1986). Applications of circumscription to formalizing common-sense knowledge. Artificial Intelligence, 28:89-116.

S. Hanks and D. McDermott (1987). Nonmonotonic logic and temporal projection. Artificial Intelligence, 33(3):379-412.

R. Reiter (1991). The frame problem in the situation calculus: a simple solution (sometimes) and a completeness result for goal regression. In Vladimir Lifschitz, editor, Artificial Intelligence and Mathematical Theory of Computation: Papers in Honor of John McCarthy, pages 359-380. Academic Press, New York.

M. Gelfond and V. Lifschitz (1993). Representing action and change by logic programs. Journal of Logic Programming, 17:301-322.

E. Sandewall (1994), Features and Fluents, Oxford University Press.

E. Sandewall and Y. Shoham (1995), Non-monotonic Temporal Reasoning, in D. M. Gabbay, C. J. Hogger and J. A. Robinson eds., Handbook of Logic in Artificial Intelligence and Logic Programming, vol. 4, ch. 7, p. 439–498, Oxford University Press.

J.A. Toth (1995). Book review. Kenneth M. and Patrick J. Hayes, eds., Reasoning agents in a dynamic world: The frame problem. Artificial Intelligence, 73:323-369.

M. Shanahan (1997). Solving the frame problem: A mathematical investigation of the common sense law of inertia. MIT Press.

P. Liberatore (1997). The complexity of the language A. Electronic Transactions on Artificial Intelligence, 1(1-3):13-37.

E. Sandewall (1998). Cognitive robotics logic and its metatheory: Features and fluents revisited. Electronic Transactions on Artificial Intelligence, 2(3-4):307-329.

M. Gelfond and V. Lifschitz (1998). Action languages. Electronic Transactions on Artificial Intelligence, 2(3-4):193-210.

H. Levesque, F. Pirri, and R. Reiter (1998). Foundations for the situation calculus. Electronic Transactions on Artificial Intelligence, 2(3-4):159-178.

F. Pirri and R. Reiter (1999). Some contributions to the metatheory of the Situation Calculus. Journal of the ACM, 46(3):325–361. 21 year-old Glazier James Grippo from Edam, enjoys hang gliding, industrial property developers in singapore developers in singapore and camping. Finds the entire world an motivating place we have spent 4 months at Alejandro de Humboldt National Park.

P. Doherty, J. Gustafsson, L. Karlsson, and J. Kvarnström (1998). TAL: Temporal action logics language specification and tutorial. Electronic Transactions on Artificial Intelligence, 2(3-4):273-306.

M. Thielscher (1998). Introduction to the fluent calculus. Electronic Transactions on Artificial Intelligence, 2(3-4):179-192.

R. Miller and M. Shanahan (1999). The event-calculus in classical logic - alternative axiomatizations. Electronic Transactions on Artificial Intelligence, 3(1):77-105.

R. Reiter (1980). A logic for default reasoning. Artificial Intelligence, 13:81-132.

H. Turner (1997) Representing actions in logic programs and default theories: a situation calculus approach. Journal of Logic Programming, 31:245-298.

V. Lifschitz (2012) The frame problem, then and now. Talk at Celebration of John McCarthy's Accomplishments, Stanford University, March 25, 2012.

External links

Template:SEP
Some Philosophical Problems from the Standpoint of Artificial Intelligence; the original article of McCarthy and Hayes that proposed the problem.

Template:John McCarthy navbox

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The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

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↑ i.e., no contradicting information is known

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In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

[2] One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

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